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cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Cari di wiki ini [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Cari</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Cari Wikipedia" aria-label="Cari Wikipedia" autocapitalize="sentences" title="Cari di wiki ini [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Khas:Cari"> </div> <button class="cdx-button cdx-search-input__end-button">Cari</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Alat peribadi"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Penampilan"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Tukar penampilan saiz, lebar dan warna fon laman" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Penampilan" > <label id="vector-appearance-dropdown-label" 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href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ms.wikipedia.org&uselang=ms" class=""><span>Derma</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Khas:Buka_akaun&returnto=Cerun" title="Anda digalakkan untuk membuka akaun dan melog masuk; walau bagaimanapun, ianya tidak wajib" class=""><span>Buka akaun</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Khas:Log_masuk&returnto=Cerun" title="Anda digalakkan untuk melog masuk; walau bagaimanapun, ia tidak wajib. [o]" accesskey="o" class=""><span>Log masuk</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Lebih pilihan" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Alat peribadi" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Alat peribadi</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="Menu pengguna" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_ms.wikipedia.org&uselang=ms"><span>Derma</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Khas:Buka_akaun&returnto=Cerun" title="Anda digalakkan untuk membuka akaun dan melog masuk; walau bagaimanapun, ianya tidak wajib"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Buka akaun</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Khas:Log_masuk&returnto=Cerun" title="Anda digalakkan untuk melog masuk; walau bagaimanapun, ia tidak wajib. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Log masuk</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Laman untuk penyunting log keluar <a href="/wiki/Bantuan:Pengenalan" aria-label="Ketahui lebih lanjut tentang menyunting"><span>Ketahui lebih lanjut</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Khas:Sumbangan_saya" title="Senarai suntingan yang dibuat daripada alamat IP ini [y]" accesskey="y"><span>Sumbangan</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Khas:Perbincangan_saya" title="Perbincangan mengenai penyuntingan daripada alamat IP anda [n]" accesskey="n"><span>Perbincangan</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Tapak"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Kandungan" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Kandungan</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">alih ke bar sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">sorokkan</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">Permulaan</div> </a> </li> <li id="toc-Takrifan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Takrifan"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Takrifan</span> </div> </a> <button aria-controls="toc-Takrifan-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Togol subbahagian Takrifan</span> </button> <ul id="toc-Takrifan-sublist" class="vector-toc-list"> <li id="toc-Contoh" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Contoh"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Contoh</span> </div> </a> <ul id="toc-Contoh-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Algebra_dan_geometri" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Algebra_dan_geometri"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Algebra dan geometri</span> </div> </a> <button aria-controls="toc-Algebra_dan_geometri-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Togol subbahagian Algebra dan geometri</span> </button> <ul id="toc-Algebra_dan_geometri-sublist" class="vector-toc-list"> <li id="toc-Contoh_2" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Contoh_2"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Contoh</span> </div> </a> <ul id="toc-Contoh_2-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Perangkaan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Perangkaan"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Perangkaan</span> </div> </a> <ul id="toc-Perangkaan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Cerun_jalan_atau_kereta_api" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Cerun_jalan_atau_kereta_api"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Cerun jalan atau kereta api</span> </div> </a> <ul id="toc-Cerun_jalan_atau_kereta_api-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kalkulus" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kalkulus"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Kalkulus</span> </div> </a> <ul id="toc-Kalkulus-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lihat_juga" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Lihat_juga"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Lihat juga</span> </div> </a> <ul id="toc-Lihat_juga-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Rujukan" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Rujukan"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>Rujukan</span> </div> </a> <ul id="toc-Rujukan-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Pautan_luar" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Pautan_luar"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>Pautan luar</span> </div> </a> <ul id="toc-Pautan_luar-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="Kandungan" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Togol isi kandungan" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">Togol isi kandungan</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">Cerun</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Pergi ke rencana dalam bahasa lain. Tersedia dalam 66 bahasa" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-66" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">66 bahasa</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-am mw-list-item"><a href="https://am.wikipedia.org/wiki/%E1%8A%A9%E1%88%AD%E1%89%A3" title="ኩርባ – Amharic" lang="am" hreflang="am" data-title="ኩርባ" data-language-autonym="አማርኛ" data-language-local-name="Amharic" class="interlanguage-link-target"><span>አማርኛ</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%85%D9%8A%D9%84_%D8%A7%D9%84%D9%85%D8%B3%D8%AA%D9%82%D9%8A%D9%85" title="ميل المستقيم – Arab" lang="ar" hreflang="ar" data-title="ميل المستقيم" data-language-autonym="العربية" data-language-local-name="Arab" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/Bucaq_%C9%99msal%C4%B1" title="Bucaq əmsalı – Azerbaijan" lang="az" hreflang="az" data-title="Bucaq əmsalı" data-language-autonym="Azərbaycanca" data-language-local-name="Azerbaijan" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Kemiringan" title="Kemiringan – Indonesia" lang="id" hreflang="id" data-title="Kemiringan" data-language-autonym="Bahasa Indonesia" data-language-local-name="Indonesia" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%A2%E0%A6%BE%E0%A6%B2" title="ঢাল – Benggali" lang="bn" hreflang="bn" data-title="ঢাল" data-language-autonym="বাংলা" data-language-local-name="Benggali" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/Si%C3%A2-lu%CC%8Dt" title="Siâ-lu̍t – Cina Min Nan" lang="nan" hreflang="nan" data-title="Siâ-lu̍t" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Cina Min Nan" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%94%D0%B8%D1%84%D0%B5%D1%80%D0%B5%D0%BD%D1%87%D0%BD%D0%BE_%D1%87%D0%B0%D1%81%D1%82%D0%BD%D0%BE" title="Диференчно частно – Bulgaria" lang="bg" hreflang="bg" data-title="Диференчно частно" data-language-autonym="Български" data-language-local-name="Bulgaria" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Pendent_(matem%C3%A0tiques)" title="Pendent (matemàtiques) – Catalonia" lang="ca" hreflang="ca" data-title="Pendent (matemàtiques)" data-language-autonym="Català" data-language-local-name="Catalonia" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A2%D0%B0%D0%B9%D0%BB%C4%83%D0%BC_%D0%BA%D0%BE%D1%8D%D1%84%D1%84%D0%B8%D1%86%D0%B8%D0%B5%D0%BD%D1%87%C4%95" title="Тайлăм коэффициенчĕ – Chuvash" lang="cv" hreflang="cv" data-title="Тайлăм коэффициенчĕ" data-language-autonym="Чӑвашла" data-language-local-name="Chuvash" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Sm%C4%9Brnice_p%C5%99%C3%ADmky" title="Směrnice přímky – Czech" lang="cs" hreflang="cs" data-title="Směrnice přímky" data-language-autonym="Čeština" data-language-local-name="Czech" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-sn mw-list-item"><a href="https://sn.wikipedia.org/wiki/Mawere" title="Mawere – Shona" lang="sn" hreflang="sn" data-title="Mawere" data-language-autonym="ChiShona" data-language-local-name="Shona" class="interlanguage-link-target"><span>ChiShona</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Goledd" title="Goledd – Wales" lang="cy" hreflang="cy" data-title="Goledd" data-language-autonym="Cymraeg" data-language-local-name="Wales" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/H%C3%A6ldningskoefficient" title="Hældningskoefficient – Denmark" lang="da" hreflang="da" data-title="Hældningskoefficient" data-language-autonym="Dansk" data-language-local-name="Denmark" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D8%B7%D9%8A%D9%88%D8%AD_(%D9%85%D8%A7%D8%B7)" title="طيوح (ماط) – Arab Maghribi" lang="ary" hreflang="ary" data-title="طيوح (ماط)" data-language-autonym="الدارجة" data-language-local-name="Arab Maghribi" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Steigung" title="Steigung – Jerman" lang="de" hreflang="de" data-title="Steigung" data-language-autonym="Deutsch" data-language-local-name="Jerman" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/T%C3%B5us_(matemaatika)" title="Tõus (matemaatika) – Estonia" lang="et" hreflang="et" data-title="Tõus (matemaatika)" data-language-autonym="Eesti" data-language-local-name="Estonia" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%9A%CE%BB%CE%AF%CF%83%CE%B7_%CF%83%CF%85%CE%BD%CE%AC%CF%81%CF%84%CE%B7%CF%83%CE%B7%CF%82" title="Κλίση συνάρτησης – Greek" lang="el" hreflang="el" data-title="Κλίση συνάρτησης" data-language-autonym="Ελληνικά" data-language-local-name="Greek" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Slope" title="Slope – Inggeris" lang="en" hreflang="en" data-title="Slope" data-language-autonym="English" data-language-local-name="Inggeris" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Pendiente_(matem%C3%A1tica)" title="Pendiente (matemática) – Sepanyol" lang="es" hreflang="es" data-title="Pendiente (matemática)" data-language-autonym="Español" data-language-local-name="Sepanyol" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Malda_(geometria)" title="Malda (geometria) – Basque" lang="eu" hreflang="eu" data-title="Malda (geometria)" data-language-autonym="Euskara" data-language-local-name="Basque" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D8%B4%DB%8C%D8%A8" title="شیب – Parsi" lang="fa" hreflang="fa" data-title="شیب" data-language-autonym="فارسی" data-language-local-name="Parsi" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Pente_(math%C3%A9matiques)" title="Pente (mathématiques) – Perancis" lang="fr" hreflang="fr" data-title="Pente (mathématiques)" data-language-autonym="Français" data-language-local-name="Perancis" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/F%C3%A1na" title="Fána – Ireland" lang="ga" hreflang="ga" data-title="Fána" data-language-autonym="Gaeilge" data-language-local-name="Ireland" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Pendente_(matem%C3%A1ticas)" title="Pendente (matemáticas) – Galicia" lang="gl" hreflang="gl" data-title="Pendente (matemáticas)" data-language-autonym="Galego" data-language-local-name="Galicia" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B8%B0%EC%9A%B8%EA%B8%B0" title="기울기 – Korea" lang="ko" hreflang="ko" data-title="기울기" data-language-autonym="한국어" data-language-local-name="Korea" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D5%88%D6%82%D5%B2%D5%B2%D5%AB_%D5%A1%D5%B6%D5%AF%D5%B5%D5%B8%D6%82%D5%B6%D5%A1%D5%B5%D5%AB%D5%B6_%D5%A3%D5%B8%D6%80%D5%AE%D5%A1%D5%AF%D5%AB%D6%81" title="Ուղղի անկյունային գործակից – Armenia" lang="hy" hreflang="hy" data-title="Ուղղի անկյունային գործակից" data-language-autonym="Հայերեն" data-language-local-name="Armenia" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%B5%E0%A4%A3%E0%A4%A4%E0%A4%BE" title="प्रवणता – Hindi" lang="hi" hreflang="hi" data-title="प्रवणता" data-language-autonym="हिन्दी" data-language-local-name="Hindi" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Koeficijent_smjera_pravca" title="Koeficijent smjera pravca – Croatia" lang="hr" hreflang="hr" data-title="Koeficijent smjera pravca" data-language-autonym="Hrvatski" data-language-local-name="Croatia" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Pento" title="Pento – Ido" lang="io" hreflang="io" data-title="Pento" data-language-autonym="Ido" data-language-local-name="Ido" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Hallatala" title="Hallatala – Iceland" lang="is" hreflang="is" data-title="Hallatala" data-language-autonym="Íslenska" data-language-local-name="Iceland" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Coefficiente_angolare" title="Coefficiente angolare – Itali" lang="it" hreflang="it" data-title="Coefficiente angolare" data-language-autonym="Italiano" data-language-local-name="Itali" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%A9%D7%99%D7%A4%D7%95%D7%A2" title="שיפוע – Ibrani" lang="he" hreflang="he" data-title="שיפוע" data-language-autonym="עברית" data-language-local-name="Ibrani" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%93%E0%B2%9F_(%E0%B2%97%E0%B2%A3%E0%B2%BF%E0%B2%A4%E0%B2%B6%E0%B2%BE%E0%B2%B8%E0%B3%8D%E0%B2%A4%E0%B3%8D%E0%B2%B0%E0%B2%A6%E0%B2%B2%E0%B3%8D%E0%B2%B2%E0%B2%BF)" title="ಓಟ (ಗಣಿತಶಾಸ್ತ್ರದಲ್ಲಿ) – Kannada" lang="kn" hreflang="kn" data-title="ಓಟ (ಗಣಿತಶಾಸ್ತ್ರದಲ್ಲಿ)" data-language-autonym="ಕನ್ನಡ" data-language-local-name="Kannada" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%91%D2%B1%D1%80%D1%8B%D1%88%D1%82%D1%8B%D2%9B_%D0%BA%D0%BE%D1%8D%D1%84%D1%84%D0%B8%D1%86%D0%B8%D0%B5%D0%BD%D1%82" title="Бұрыштық коэффициент – Kazakhstan" lang="kk" hreflang="kk" data-title="Бұрыштық коэффициент" data-language-autonym="Қазақша" data-language-local-name="Kazakhstan" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Krypties_koeficientas" title="Krypties koeficientas – Lithuania" lang="lt" hreflang="lt" data-title="Krypties koeficientas" data-language-autonym="Lietuvių" data-language-local-name="Lithuania" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-li mw-list-item"><a href="https://li.wikipedia.org/wiki/Riechtingsco%C3%ABffici%C3%ABnt" title="Riechtingscoëfficiënt – Limburgish" lang="li" hreflang="li" data-title="Riechtingscoëfficiënt" data-language-autonym="Limburgs" data-language-local-name="Limburgish" class="interlanguage-link-target"><span>Limburgs</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%9D%D0%B0%D0%BA%D0%BB%D0%BE%D0%BD_(%D0%BC%D0%B0%D1%82%D0%B5%D0%BC%D0%B0%D1%82%D0%B8%D0%BA%D0%B0)" title="Наклон (математика) – Macedonia" lang="mk" hreflang="mk" data-title="Наклон (математика)" data-language-autonym="Македонски" data-language-local-name="Macedonia" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%86%E0%B4%A8%E0%B4%A4%E0%B4%BF" title="ആനതി – Malayalam" lang="ml" hreflang="ml" data-title="ആനതി" data-language-autonym="മലയാളം" data-language-local-name="Malayalam" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%AA%E0%A5%8D%E0%A4%B0%E0%A4%B5%E0%A4%A3%E0%A4%A4%E0%A4%BE_(%E0%A4%AC%E0%A5%80%E0%A4%9C%E0%A4%97%E0%A4%A3%E0%A4%BF%E0%A4%A4)" title="प्रवणता (बीजगणित) – Marathi" lang="mr" hreflang="mr" data-title="प्रवणता (बीजगणित)" data-language-autonym="मराठी" data-language-local-name="Marathi" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Richtingsco%C3%ABffici%C3%ABnt" title="Richtingscoëfficiënt – Belanda" lang="nl" hreflang="nl" data-title="Richtingscoëfficiënt" data-language-autonym="Nederlands" data-language-local-name="Belanda" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E5%82%BE%E3%81%8D_(%E6%95%B0%E5%AD%A6)" title="傾き (数学) – Jepun" lang="ja" hreflang="ja" data-title="傾き (数学)" data-language-autonym="日本語" data-language-local-name="Jepun" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Stigningstall" title="Stigningstall – Bokmal Norway" lang="nb" hreflang="nb" data-title="Stigningstall" data-language-autonym="Norsk bokmål" data-language-local-name="Bokmal Norway" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-om mw-list-item"><a href="https://om.wikipedia.org/wiki/Dhundhula" title="Dhundhula – Oromo" lang="om" hreflang="om" data-title="Dhundhula" data-language-autonym="Oromoo" data-language-local-name="Oromo" class="interlanguage-link-target"><span>Oromoo</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Burchak_koeffitsiyenti" title="Burchak koeffitsiyenti – Uzbekistan" lang="uz" hreflang="uz" data-title="Burchak koeffitsiyenti" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbekistan" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Nachylenie" title="Nachylenie – Poland" lang="pl" hreflang="pl" data-title="Nachylenie" data-language-autonym="Polski" data-language-local-name="Poland" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Declive" title="Declive – Portugis" lang="pt" hreflang="pt" data-title="Declive" data-language-autonym="Português" data-language-local-name="Portugis" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Pant%C4%83" title="Pantă – Romania" lang="ro" hreflang="ro" data-title="Pantă" data-language-autonym="Română" data-language-local-name="Romania" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A3%D0%B3%D0%BB%D0%BE%D0%B2%D0%BE%D0%B9_%D0%BA%D0%BE%D1%8D%D1%84%D1%84%D0%B8%D1%86%D0%B8%D0%B5%D0%BD%D1%82" title="Угловой коэффициент – Rusia" lang="ru" hreflang="ru" data-title="Угловой коэффициент" data-language-autonym="Русский" data-language-local-name="Rusia" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Pjerr%C3%ABsia" title="Pjerrësia – Albania" lang="sq" hreflang="sq" data-title="Pjerrësia" data-language-autonym="Shqip" data-language-local-name="Albania" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Slope_(mathematics)" title="Slope (mathematics) – Simple English" lang="en-simple" hreflang="en-simple" data-title="Slope (mathematics)" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Smernica_priamky" title="Smernica priamky – Slovak" lang="sk" hreflang="sk" data-title="Smernica priamky" data-language-autonym="Slovenčina" data-language-local-name="Slovak" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D9%84%DB%8E%DA%98%DB%8C" title="لێژی – Kurdi Tengah" lang="ckb" hreflang="ckb" data-title="لێژی" data-language-autonym="کوردی" data-language-local-name="Kurdi Tengah" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%9A%D0%BE%D0%B5%D1%84%D0%B8%D1%86%D0%B8%D1%98%D0%B5%D0%BD%D1%82_%D0%BF%D1%80%D0%B0%D0%B2%D1%86%D0%B0" title="Коефицијент правца – Serbia" lang="sr" hreflang="sr" data-title="Коефицијент правца" data-language-autonym="Српски / srpski" data-language-local-name="Serbia" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Kulmakerroin" title="Kulmakerroin – Finland" lang="fi" hreflang="fi" data-title="Kulmakerroin" data-language-autonym="Suomi" data-language-local-name="Finland" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Riktningskoefficient" title="Riktningskoefficient – Sweden" lang="sv" hreflang="sv" data-title="Riktningskoefficient" data-language-autonym="Svenska" data-language-local-name="Sweden" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Lihis" title="Lihis – Tagalog" lang="tl" hreflang="tl" data-title="Lihis" data-language-autonym="Tagalog" data-language-local-name="Tagalog" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%9A%E0%AE%BE%E0%AE%AF%E0%AF%8D%E0%AE%B5%E0%AF%81" title="சாய்வு – Tamil" lang="ta" hreflang="ta" data-title="சாய்வு" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-kab mw-list-item"><a href="https://kab.wikipedia.org/wiki/Asekser_(tusnakt)" title="Asekser (tusnakt) – Kabyle" lang="kab" hreflang="kab" data-title="Asekser (tusnakt)" data-language-autonym="Taqbaylit" data-language-local-name="Kabyle" class="interlanguage-link-target"><span>Taqbaylit</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%84%E0%B8%A7%E0%B8%B2%E0%B8%A1%E0%B8%8A%E0%B8%B1%E0%B8%99" title="ความชัน – Thai" lang="th" hreflang="th" data-title="ความชัน" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/%C4%90%E1%BB%99_d%E1%BB%91c" title="Độ dốc – Vietnam" lang="vi" hreflang="vi" data-title="Độ dốc" data-language-autonym="Tiếng Việt" data-language-local-name="Vietnam" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/E%C4%9Fim" title="Eğim – Turki" lang="tr" hreflang="tr" data-title="Eğim" data-language-autonym="Türkçe" data-language-local-name="Turki" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%9A%D1%83%D1%82%D0%BE%D0%B2%D0%B8%D0%B9_%D0%BA%D0%BE%D0%B5%D1%84%D1%96%D1%86%D1%96%D1%94%D0%BD%D1%82" title="Кутовий коефіцієнт – Ukraine" lang="uk" hreflang="uk" data-title="Кутовий коефіцієнт" data-language-autonym="Українська" data-language-local-name="Ukraine" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh-classical mw-list-item"><a href="https://zh-classical.wikipedia.org/wiki/%E6%96%9C%E7%8E%87" title="斜率 – Literary Chinese" lang="lzh" hreflang="lzh" data-title="斜率" data-language-autonym="文言" data-language-local-name="Literary Chinese" class="interlanguage-link-target"><span>文言</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%96%9C%E7%8E%87" title="斜率 – Cina Wu" lang="wuu" hreflang="wuu" data-title="斜率" data-language-autonym="吴语" data-language-local-name="Cina Wu" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%96%9C%E7%8E%87" title="斜率 – Kantonis" lang="yue" hreflang="yue" data-title="斜率" data-language-autonym="粵語" data-language-local-name="Kantonis" class="interlanguage-link-target"><span>粵語</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%96%9C%E7%8E%87" title="斜率 – Cina" lang="zh" hreflang="zh" data-title="斜率" data-language-autonym="中文" data-language-local-name="Cina" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q275447#sitelinks-wikipedia" title="Sunting pautan antara bahasa" class="wbc-editpage">Sunting pautan</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="Ruang nama"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/Cerun" title="Lihat laman kandungan [c]" accesskey="c"><span>Rencana</span></a></li><li id="ca-talk" class="new vector-tab-noicon mw-list-item"><a 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buku</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Khas:DownloadAsPdf&page=Cerun&action=show-download-screen"><span>Muat turun sebagai PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=Cerun&printable=yes" title="Versi boleh cetak bagi laman ini [p]" accesskey="p"><span>Versi boleh cetak</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Dalam projek lain </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q275447" title="Pautan ke item repositori data yang bersambung [g]" accesskey="g"><span>Butir Wikidata</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Alatan laman"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Penampilan"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Penampilan</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">alih ke bar sisi</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">sorokkan</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">Daripada Wikipedia, ensiklopedia bebas.</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="ms" dir="ltr"><figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fail:Wiki_slope_in_2d.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Wiki_slope_in_2d.svg/220px-Wiki_slope_in_2d.svg.png" decoding="async" width="220" height="237" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Wiki_slope_in_2d.svg/330px-Wiki_slope_in_2d.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c1/Wiki_slope_in_2d.svg/440px-Wiki_slope_in_2d.svg.png 2x" data-file-width="281" data-file-height="303" /></a><figcaption> Cerun: <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {\Delta y}{\Delta x}}=\tan(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {\Delta y}{\Delta x}}=\tan(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/98d19d47ccaae2f4027a94e0b7ca6c8434d7685e" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:18.598ex; height:5.676ex;" alt="{\displaystyle m={\frac {\Delta y}{\Delta x}}=\tan(\theta )}"></span></figcaption></figure> <p>Dalam matematik, <b>cerun</b> (<a href="/wiki/Tulisan_Jawi" title="Tulisan Jawi">Jawi</a>: <span dir="rtl" style="font-size:100%;">‏<span title="Melayu (bahasa makro)-language text"><span lang="ms"><style data-mw-deduplicate="TemplateStyles:r5953951">.mw-parser-output .script-Adlm{font-family:"Noto Sans Adlam"}.mw-parser-output .script-Aghb{font-family:"Noto Sans Caucasian Albanian"}.mw-parser-output .script-Ahom{font-family:"Noto Serif Ahom"}.mw-parser-output .script-Arab{font-family:"Scheherazade New",Scheherazade,Lateef,LateefGR,Amiri,"Noto Naskh 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.script-Cyrs{font-family:"Ponomar Unicode","Ponomar Unicode TT","Acathist","Triodion Unicode","Menaion Unicode","Menaion Unicode TT","Shafarik","Fedorovsk Unicode","Fedorovsk Unicode TT","Monomakh Unicode","Monomakh Unicode TT",BukyVede,"Kliment Std","RomanCyrillic Std","Monomachus","Old Standard","Old Standard TT",Dilyana,Menaion,"Menaion Medieval",Lazov,Code2000,"DejaVu Sans","DejaVu Serif",Code2001,"FreeSerif","TITUS Cyberbit Basic","Charis SIL","Doulos SIL","Chrysanthi Unicode","Bitstream Cyberbit","Bitstream CyberBase",Thryomanes,"Lucida Grande","FreeSans","Arial Unicode MS","Microsoft Sans Serif","Lucida Sans Unicode"}</style><span class="script-Arab" dir="rtl" style="font-size: 125%;"><b>چرون</b></span>‎</span></span><span class="lang-comment" style="font-style: normal; display: none; color: #33aa33; margin-left: 0.3em;">code: ms is deprecated </span>‎</span>) atau <b>kecerunan</b> (<a href="/wiki/Tulisan_Jawi" title="Tulisan Jawi">Jawi</a>: <span dir="rtl" style="font-size:100%;">‏<span title="Melayu (bahasa makro)-language text"><span lang="ms"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5953951"><span class="script-Arab" dir="rtl" style="font-size: 125%;"><b>کچرونن</b></span>‎</span></span><span class="lang-comment" style="font-style: normal; display: none; color: #33aa33; margin-left: 0.3em;">code: ms is deprecated </span>‎</span>) <a href="/wiki/Garis_(geometri)" title="Garis (geometri)">garis</a> ialah nombor yang menerangkan kedua-dua <i>arah</i> dan <i>kecuraman</i> sesuatu garis.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Cerun sering dilambangkan dengan huruf <i>m</i>; tiada jawapan yang jelas kepada soalan mengapa huruf <i>m</i> digunakan untuk cerun, tetapi penggunaan terawalnya dalam bahasa Inggeris terdapat dalam O'Brien (1844)<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> yang menulis persamaan garis lurus sebagai <span class="nowrap">"<i>y</i> = <i>mx</i> + <i>b</i>"</span> dan ia juga boleh didapati dalam Todhunter (1888)<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> yang menulisnya sebagai " <i>y</i> = <i>mx</i> + <i>c</i> ".<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> </p><p>Cerun dikira dengan mencari <a href="/wiki/Nisbah" title="Nisbah">nisbah</a> "perubahan menegak" kepada "perubahan mendatar" antara (mana-mana) dua titik berbeza pada satu garis. Kadang kala nisbah dinyatakan sebagai hasil bahagi ("naik atas larian"), memberikan nombor yang sama untuk setiap dua titik berbeza pada baris yang sama. Garisan yang semakin menurun mempunyai "kenaikan" negatif. Garisan itu mungkin praktikal – seperti yang ditetapkan oleh <a href="/wiki/Ilmu_ukur" title="Ilmu ukur">juruukur jalan</a>, atau dalam <a href="/wiki/Rajah" title="Rajah">rajah</a> yang memodelkan jalan atau bumbung sama ada sebagai penerangan atau sebagai pelan. </p><p><i>Kecuraman</i>, kecondongan atau gred garisan diukur dengan <a href="/wiki/Nilai_mutlak" title="Nilai mutlak">nilai mutlak</a> cerun. Cerun dengan nilai mutlak yang lebih besar menunjukkan garis yang lebih curam. <i>Arah</i> <a href="/wiki/Garis_(geometri)" title="Garis (geometri)">garis</a> sama ada meningkat, menurun, mendatar atau menegak. </p> <ul><li>Garis <b>menaik</b> jika ia <b>naik</b> dari kiri ke kanan. Cerun adalah <b>positif</b>, iaitu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m>0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>></mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m>0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/501173910e6da8425b4e9d44a4e8643620bc2464" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.301ex; height:2.176ex;" alt="{\displaystyle m>0}"></span>.</li> <li>Garis <b>menurun</b> jika ia <b>turun</b> dari kiri ke kanan. Cerun adalah <b>negatif</b>, iaitu <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m<0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo><</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m<0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6ba378205efd9dc579591efdd5baa301f4f6e2fa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.301ex; height:2.176ex;" alt="{\displaystyle m<0}"></span>.</li> <li>Jika garisan mendatar, kecerunannya ialah <b>sifar</b>. Ini adalah <a href="/w/index.php?title=Fungsi_malar&action=edit&redlink=1" class="new" title="Fungsi malar (laman tidak wujud)">fungsi malar</a>.</li> <li>Jika garisan menegak, cerun <i>tidak tertakrif</i> (lihat di bawah).</li></ul> <p>Kenaikan jalan di antara dua titik ialah perbezaan antara ketinggian jalan di dua titik tersebut, katakan <i>y</i> <sub>1</sub> dan <i>y</i> <sub>2</sub>, atau dengan kata lain, kenaikan ialah (<i>y</i><sub>2</sub> − <i>y</i><sub>1</sub>) = Δ<i>y</i>. Untuk jarak yang agak pendek, di mana kelengkungan Bumi mungkin diabaikan, larian ialah perbezaan jarak dari titik tetap yang diukur sepanjang aras, garis mendatar, atau dengan kata lain, larian ialah (<i>x</i><sub>2</sub> − <i>x</i><sub>1</sub>) = Δ<i>x</i>. Di sini kecerunan jalan di antara dua titik hanya digambarkan sebagai nisbah perubahan ketinggian kepada jarak mendatar antara mana-mana dua titik pada garisan. </p><p>Dalam bahasa matematik, kecerunan <i>m</i> garis ialah </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72263d5113a7cc985f29fc9fc4b3f5e85dd5bbe5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.23ex; height:5.509ex;" alt="{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}"></span></dd></dl> <p>Konsep cerun terpakai terus kepada <a href="/w/index.php?title=Gred_(kecerunan)&action=edit&redlink=1" class="new" title="Gred (kecerunan) (laman tidak wujud)">gred</a> atau <a href="/w/index.php?title=Gradien&action=edit&redlink=1" class="new" title="Gradien (laman tidak wujud)">gradien</a> dalam <a href="/wiki/Geografi" title="Geografi">geografi</a> dan <a href="/wiki/Kejuruteraan_awam" title="Kejuruteraan awam">kejuruteraan awam</a>. Melalui <a href="/wiki/Trigonometri" title="Trigonometri">trigonometri</a>, kecerunan <i>m</i> garis dikaitkan dengan <a href="/wiki/Sudut" title="Sudut">sudut</a> kecondongannya <i>θ</i> oleh <a href="/wiki/Fungsi_trigonometri" title="Fungsi trigonometri">fungsi tangen.</a> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=\tan(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\tan(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e53a5ce7db600961ae411d4d1fbef636a62ddb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.398ex; height:2.843ex;" alt="{\displaystyle m=\tan(\theta )}"></span></dd></dl> <p>Oleh itu, garisan menaik 45° mempunyai kecerunan +1 dan garis menurun 45° mempunyai kecerunan sebanyak −1. </p><p>Sebagai pengitlakan penerangan praktikal ini, matematik <a href="/w/index.php?title=Kalkulus_pembezaan&action=edit&redlink=1" class="new" title="Kalkulus pembezaan (laman tidak wujud)">kalkulus pembezaan</a> menakrifkan <a href="/wiki/Lengkung" title="Lengkung">kecerunan</a> lengkung pada satu titik sebagai kecerunan <a href="/wiki/Tangen" title="Tangen">garis tangen</a> pada titik itu. Apabila lengkung diberikan oleh satu siri titik dalam rajah atau dalam senarai koordinat titik, cerun boleh dikira bukan pada satu titik tetapi di antara mana-mana dua titik tertentu. Apabila lengkung diberikan sebagai <a href="/wiki/Fungsi_selanjar" title="Fungsi selanjar">fungsi selanjar</a>, mungkin sebagai <a href="/wiki/Ungkapan_algebra" title="Ungkapan algebra">ungkapan algebra</a>, maka kalkulus pembezaan menyediakan peraturan yang memberikan formula untuk kecerunan lengkung pada mana-mana titik di tengah lengkung. </p><p>Pengitlakan konsep cerun ini membolehkan pembinaan yang sangat kompleks dirancang dan dibina yang melampaui struktur statik yang sama ada mendatar atau menegak, tetapi boleh berubah mengikut masa, bergerak dalam lengkung, dan berubah bergantung pada kadar perubahan faktor lain. Oleh itu, idea mudah cerun menjadi salah satu asas utama dunia moden dari segi teknologi dan persekitaran binaan. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Takrifan">Takrifan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=1" title="Sunting bahagian: Takrifan" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=1" title="Sunting kod sumber bahagian: Takrifan"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fail:Slope_of_lines_illustrated.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Slope_of_lines_illustrated.jpg/400px-Slope_of_lines_illustrated.jpg" decoding="async" width="400" height="303" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/bf/Slope_of_lines_illustrated.jpg/600px-Slope_of_lines_illustrated.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/b/bf/Slope_of_lines_illustrated.jpg 2x" data-file-width="609" data-file-height="462" /></a><figcaption> Cerun digambarkan untuk <span class="nowrap"><i>y</i> = (3/2)<i>x</i> − 1</span>. Klik untuk membesarkan</figcaption></figure> <figure class="mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/Fail:Gradient_of_a_line_in_coordinates_from_-12x%2B2_to_%2B12x%2B2.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/a/aa/Gradient_of_a_line_in_coordinates_from_-12x%2B2_to_%2B12x%2B2.gif/400px-Gradient_of_a_line_in_coordinates_from_-12x%2B2_to_%2B12x%2B2.gif" decoding="async" width="400" height="400" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/a/aa/Gradient_of_a_line_in_coordinates_from_-12x%2B2_to_%2B12x%2B2.gif 1.5x" data-file-width="600" data-file-height="600" /></a><figcaption>Kecerunan garis dalam sistem koordinat, dari <span class="nowrap"><i>f</i>(<i>x</i>) = −12<i>x</i> + 2</span> hingga <span class="nowrap"><i>f</i>(<i>x</i>) = 12<i>x</i> + 2</span></figcaption></figure> <p>Kecerunan garis dalam satah yang mengandungi paksi <i>x</i> dan <i>y</i> secara amnya diwakili oleh huruf <i>m</i>, dan ditakrifkan sebagai perubahan dalam koordinat <i>y</i> dibahagikan dengan perubahan sepadan dalam koordinat <i>x</i>, antara dua titik berbeza pada garisan. Ini dijelaskan oleh persamaan berikut: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {\Delta y}{\Delta x}}={\frac {{\text{perubahan}}\,{\text{menegak}}}{{\text{perubahan}}\,{\text{mengufuk}}}}={\frac {\text{naikan}}{\text{larian}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>perubahan</mtext> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>menegak</mtext> </mrow> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mtext>perubahan</mtext> </mrow> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mtext>mengufuk</mtext> </mrow> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>naikan</mtext> <mtext>larian</mtext> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {\Delta y}{\Delta x}}={\frac {{\text{perubahan}}\,{\text{menegak}}}{{\text{perubahan}}\,{\text{mengufuk}}}}={\frac {\text{naikan}}{\text{larian}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/780ba14bd06158164798aaf1c53b3f6096577884" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:45.607ex; height:6.009ex;" alt="{\displaystyle m={\frac {\Delta y}{\Delta x}}={\frac {{\text{perubahan}}\,{\text{menegak}}}{{\text{perubahan}}\,{\text{mengufuk}}}}={\frac {\text{naikan}}{\text{larian}}}.}"></span></dd></dl> <p>(Huruf Yunani <i><a href="/wiki/Delta_(huruf)" title="Delta (huruf)">delta</a></i>, Δ, biasanya digunakan dalam matematik untuk bermaksud "perbezaan" atau "perubahan". ) </p><p>Diberi dua mata <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{1},y_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{1},y_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fc74086e56542bd28b46a84faaee3cebdd4a899" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.421ex; height:2.843ex;" alt="{\displaystyle (x_{1},y_{1})}"></span> dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{2},y_{2})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{2},y_{2})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d52d44e16a796acee486af49af05f678566d181a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.421ex; height:2.843ex;" alt="{\displaystyle (x_{2},y_{2})}"></span>, perubahan dalam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> dari satu ke yang lain adalah <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x_{2}-x_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x_{2}-x_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf4533d7a48189633a07785ff3fac0dcc852d515" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.608ex; height:2.343ex;" alt="{\displaystyle x_{2}-x_{1}}"></span> (<i>larian</i>), manakala perubahan dalam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> ialah <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y_{2}-y_{1}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y_{2}-y_{1}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/172550f94371f0e63473266a49766c04df02e309" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:7.227ex; height:2.343ex;" alt="{\displaystyle y_{2}-y_{1}}"></span> (<i>naikan</i>). Menggantikan kedua-dua kuantiti ke dalam persamaan di atas menghasilkan formula: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/72263d5113a7cc985f29fc9fc4b3f5e85dd5bbe5" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:14.23ex; height:5.509ex;" alt="{\displaystyle m={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}.}"></span></dd></dl> <p>Formula gagal untuk garis menegak, selari dengan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> paksi (lihat <a href="/w/index.php?title=Pembahagian_dengan_sifar&action=edit&redlink=1" class="new" title="Pembahagian dengan sifar (laman tidak wujud)">Pembahagian dengan sifar</a>), yang cerun boleh diambil sebagai <a href="/wiki/Ketakterhinggaan" title="Ketakterhinggaan">tak terhingga</a>, jadi cerun garis menegak dianggap tidak tertakrif. </p> <div class="mw-heading mw-heading3"><h3 id="Contoh">Contoh</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=2" title="Sunting bahagian: Contoh" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=2" title="Sunting kod sumber bahagian: Contoh"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Katakan satu garisan melalui dua titik: <i>P</i> = (1, 2) dan <i>Q</i> = (13, 8). Dengan membahagikan perbezaan dalam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> -koordinat mengikut perbezaan dalam <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> -koordinat, seseorang boleh mendapatkan cerun garisan: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {\Delta y}{\Delta x}}={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}={\frac {8-2}{13-1}}={\frac {6}{12}}={\frac {1}{2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> <mrow> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>8</mn> <mo>−</mo> <mn>2</mn> </mrow> <mrow> <mn>13</mn> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>6</mn> <mn>12</mn> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {\Delta y}{\Delta x}}={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}={\frac {8-2}{13-1}}={\frac {6}{12}}={\frac {1}{2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8bf2e9751b52032c289bc90ecd889be763598539" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:42.402ex; height:5.843ex;" alt="{\displaystyle m={\frac {\Delta y}{\Delta x}}={\frac {y_{2}-y_{1}}{x_{2}-x_{1}}}={\frac {8-2}{13-1}}={\frac {6}{12}}={\frac {1}{2}}}"></span>.</dd> <dd>Oleh kerana cerun adalah positif, arah garisan semakin meningkat. Memandangkan |<i>m</i>| < 1, condong tidak terlalu curam (condong < 45°).</dd></dl> <p>Sebagai contoh lain, pertimbangkan garis yang melalui titik (4, 15) dan (3, 21). Kemudian, kecerunan garisan ialah </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {21-15}{3-4}}={\frac {6}{-1}}=-6.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>21</mn> <mo>−</mo> <mn>15</mn> </mrow> <mrow> <mn>3</mn> <mo>−</mo> <mn>4</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>6</mn> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>=</mo> <mo>−</mo> <mn>6.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {21-15}{3-4}}={\frac {6}{-1}}=-6.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/69cef55373bce032897a822809760033130b958f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:27.086ex; height:5.343ex;" alt="{\displaystyle m={\frac {21-15}{3-4}}={\frac {6}{-1}}=-6.}"></span></dd> <dd>Oleh kerana cerun adalah negatif, arah garisan semakin berkurangan. Memandangkan |<i>m</i>| > 1, penurunan ini agak curam (penurunan > 45°).</dd></dl> <div class="mw-heading mw-heading2"><h2 id="Algebra_dan_geometri">Algebra dan geometri</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=3" title="Sunting bahagian: Algebra dan geometri" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=3" title="Sunting kod sumber bahagian: Algebra dan geometri"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/Fail:Slopes_of_Parallel_and_Perpendicular_Lines.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Slopes_of_Parallel_and_Perpendicular_Lines.svg/220px-Slopes_of_Parallel_and_Perpendicular_Lines.svg.png" decoding="async" width="220" height="293" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Slopes_of_Parallel_and_Perpendicular_Lines.svg/330px-Slopes_of_Parallel_and_Perpendicular_Lines.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/7a/Slopes_of_Parallel_and_Perpendicular_Lines.svg/440px-Slopes_of_Parallel_and_Perpendicular_Lines.svg.png 2x" data-file-width="324" data-file-height="432" /></a><figcaption> Cerun garis selari dan serenjang</figcaption></figure> <div><ul><li>Jika <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span> ialah <a href="/wiki/Fungsi_linear" title="Fungsi linear">fungsi linear</a> bagi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span>, maka pekali bagi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>x</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\displaystyle x}"></span> ialah kecerunan garis yang dicipta dengan memplot fungsi tersebut. Oleh itu, jika persamaan garis diberikan dalam bentuk <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=mx+b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>m</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=mx+b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25e966621217067985694be3afd6801d7d51c5d8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.462ex; height:2.509ex;" alt="{\displaystyle y=mx+b}"></span></dd></dl> maka <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> ialah cerun. Bentuk persamaan garis ini dipanggil <i>bentuk pintasan cerun</i>, kerana <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span> boleh ditafsirkan sebagai <a href="/w/index.php?title=Pintasan-y&action=edit&redlink=1" class="new" title="Pintasan-y (laman tidak wujud)">pintasan-y</a> pada garis itu, iaitu, koordinat <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span>di mana garis itu bersilang dengan paksi <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\displaystyle y}"></span>.</li><li>Jika kecerunan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0a07d98bb302f3856cbabc47b2b9016692e3f7bc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.04ex; height:1.676ex;" alt="{\displaystyle m}"></span> bagi garis dan titik <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle (x_{1},y_{1})}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>,</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (x_{1},y_{1})}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7fc74086e56542bd28b46a84faaee3cebdd4a899" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.421ex; height:2.843ex;" alt="{\displaystyle (x_{1},y_{1})}"></span> pada garis kedua-duanya diketahui, maka persamaan garis boleh didapati menggunakan <a href="/w/index.php?title=Persamaan_Linear&action=edit&redlink=1" class="new" title="Persamaan Linear (laman tidak wujud)">rumus titik-cerun</a>: <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y-y_{1}=m(x-x_{1}).}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>−</mo> <msub> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mi>m</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <msub> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> <mo stretchy="false">)</mo> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y-y_{1}=m(x-x_{1}).}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/84a3deeceb6e8b3edabb2a7fdf8d8f77e3080e01" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.338ex; height:2.843ex;" alt="{\displaystyle y-y_{1}=m(x-x_{1}).}"></span></dd></dl></li><li>Kecerunan garis yang ditakrifkan oleh <a href="/wiki/Persamaan_linear" title="Persamaan linear">persamaan linear</a> <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle ax+by+c=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <mi>x</mi> <mo>+</mo> <mi>b</mi> <mi>y</mi> <mo>+</mo> <mi>c</mi> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ax+by+c=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/26ffa3f9c01bec425db7c1acc330497b6831697b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:15.661ex; height:2.509ex;" alt="{\displaystyle ax+by+c=0}"></span></dd> ialah <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -{\frac {a}{b}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo>−</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle -{\frac {a}{b}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/07a1b25c2a624442bd2a2a60ed363c51b78f3870" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:3.874ex; height:4.843ex;" alt="{\displaystyle -{\frac {a}{b}}}"></span>.</dd></dl></li><li>Dua garis adalah <a href="/w/index.php?title=Selari_(geometri)&action=edit&redlink=1" class="new" title="Selari (geometri) (laman tidak wujud)">selari</a> jika dan hanya jika ia bukan garis yang sama (bertepatan) dan mana-mana cerunnya adalah sama atau kedua-duanya menegak dan oleh itu kedua-duanya mempunyai cerun yang tertakrif. Dua garis adalah <a href="/wiki/Serenjang" title="Serenjang">serenjang</a> jika hasil darab kecerunannya ialah −1 atau satu mempunyai kecerunan 0 (garis mendatar) dan satu lagi mempunyai kecerunan tertakrif (garis menegak).</li><li>Sudut θ antara −90° dan 90° yang dibuat oleh garis dengan paksi <i>x</i> adalah berkaitan dengan cerun <i>m</i> seperti berikut: <dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m=\tan(\theta )}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>θ</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m=\tan(\theta )}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9e53a5ce7db600961ae411d4d1fbef636a62ddb9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:11.398ex; height:2.843ex;" alt="{\displaystyle m=\tan(\theta )}"></span></dd> dan <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =\arctan(m)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mi>arctan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>m</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\arctan(m)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/59383db807d0a809de2c95650b6dd37f2a892710" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.505ex; height:2.843ex;" alt="{\displaystyle \theta =\arctan(m)}"></span>   (ini ialah fungsi songsang tangen; lihat <a href="/w/index.php?title=Fungsi_trigonometri_songsang&action=edit&redlink=1" class="new" title="Fungsi trigonometri songsang (laman tidak wujud)">fungsi trigonometri songsang</a>).</dd></dl></li></ul></div> <div class="mw-heading mw-heading3"><h3 id="Contoh_2">Contoh</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=4" title="Sunting bahagian: Contoh" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=4" title="Sunting kod sumber bahagian: Contoh"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Sebagai contoh, pertimbangkan garis yang melalui titik (2,8) dan (3,20). Garis ini mempunyai cerun, <span class="texhtml"><i>m</i></span>, iaitu </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {(20-8)}{(3-2)}}=12.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mo stretchy="false">(</mo> <mn>20</mn> <mo>−</mo> <mn>8</mn> <mo stretchy="false">)</mo> </mrow> <mrow> <mo stretchy="false">(</mo> <mn>3</mn> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> <mo>=</mo> <mn>12.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {(20-8)}{(3-2)}}=12.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/2feb369cb521542408ae5879c3ae96b9c94a0f6f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:15.043ex; height:6.509ex;" alt="{\displaystyle {\frac {(20-8)}{(3-2)}}=12.}"></span></dd></dl> <p>Seseorang kemudian boleh menulis persamaan garis, dalam bentuk cerun titik: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y-8=12(x-2)=12x-24.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>−</mo> <mn>8</mn> <mo>=</mo> <mn>12</mn> <mo stretchy="false">(</mo> <mi>x</mi> <mo>−</mo> <mn>2</mn> <mo stretchy="false">)</mo> <mo>=</mo> <mn>12</mn> <mi>x</mi> <mo>−</mo> <mn>24.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y-8=12(x-2)=12x-24.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fdba3ca88d4ebb97c1ea496ba5db017419b48dce" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.289ex; height:2.843ex;" alt="{\displaystyle y-8=12(x-2)=12x-24.}"></span></dd></dl> <p>atau: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=12x-16.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mn>12</mn> <mi>x</mi> <mo>−</mo> <mn>16.</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=12x-16.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/63f876d9b513677fb5d7a8db19d0b1b0ce94f23f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.721ex; height:2.509ex;" alt="{\displaystyle y=12x-16.}"></span></dd></dl> <p>Sudut θ antara −90° dan 90° yang dibuat oleh garis ini dengan paksi- <span class="texhtml"><i>x</i></span> ialah </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \theta =\arctan(12)\approx 85.2^{\circ }.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>θ</mi> <mo>=</mo> <mi>arctan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mn>12</mn> <mo stretchy="false">)</mo> <mo>≈</mo> <msup> <mn>85.2</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>∘</mo> </mrow> </msup> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \theta =\arctan(12)\approx 85.2^{\circ }.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e1bee9d46953d42a037955cac7373b522b1e13ab" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:23.723ex; height:2.843ex;" alt="{\displaystyle \theta =\arctan(12)\approx 85.2^{\circ }.}"></span></dd></dl> <p>Pertimbangkan dua garis: <span class="texhtml"><i>y</i> = −3<i>x</i> + 1</span> dan <span class="texhtml"><i>y</i> = −3<i>x</i> − 2</span>. Kedua-dua garisan mempunyai kecerunan <span class="texhtml"><i>m</i> = −3</span>. Mereka bukan garis yang sama. Jadi ia adalah garis selari. </p><p>Pertimbangkan dua baris <span class="texhtml"><i>y</i> = −3<i>x</i> + 1</span> dan <span class="texhtml"><i>y</i> = <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;"><i>x</i></span><span style="display:none;">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">3</span></span> − 2</span>. Kecerunan garis pertama ialah <span class="texhtml"><i>m</i><sub>1</sub> = −3</span>. Kecerunan garis kedua ialah <span class="texhtml"><i>m</i><sub>2</sub> = <span class="sfrac nowrap" style="display:inline-block; vertical-align:-0.5em; font-size:85%; text-align:center;"><span style="display:block; line-height:1em; padding:0 0.1em;">1</span><span style="display:none;">/</span><span style="display:block; line-height:1em; padding:0 0.1em; border-top:1px solid;">3</span></span></span>. Hasil darab kedua-dua cerun ini ialah −1. Jadi kedua-dua garis ini berserenjang. </p> <div class="mw-heading mw-heading2"><h2 id="Perangkaan">Perangkaan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=5" title="Sunting bahagian: Perangkaan" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=5" title="Sunting kod sumber bahagian: Perangkaan"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Dalam <a href="/wiki/Perangkaan" title="Perangkaan">statistik</a>, kecerunan garis <a href="/w/index.php?title=Kuasa_dua_terkecil_linear&action=edit&redlink=1" class="new" title="Kuasa dua terkecil linear (laman tidak wujud)">regresi kuasa dua terkecil</a> <a href="/w/index.php?title=Padanan_garis&action=edit&redlink=1" class="new" title="Padanan garis (laman tidak wujud)">yang paling padan</a> untuk sampel data tertentu boleh ditulis sebagai: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {rs_{y}}{s_{x}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>r</mi> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mrow> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {rs_{y}}{s_{x}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b741fefbfb6a540afd9828f43870a6c551875ccd" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:9.163ex; height:5.343ex;" alt="{\displaystyle m={\frac {rs_{y}}{s_{x}}}}"></span> ,</dd></dl> <p>Kuantiti <i>m</i> ini dipanggil sebagai <i><a href="/wiki/Regresi_linear" title="Regresi linear">cerun regresi</a></i> untuk garisan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle y=mx+c}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>y</mi> <mo>=</mo> <mi>m</mi> <mi>x</mi> <mo>+</mo> <mi>c</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle y=mx+c}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/3daca9fbcf73b8a2b575a10e2d5de25f9f1c6f49" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:11.471ex; height:2.343ex;" alt="{\displaystyle y=mx+c}"></span>. Kuantiti <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle r}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>r</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle r}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0d1ecb613aa2984f0576f70f86650b7c2a132538" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.049ex; height:1.676ex;" alt="{\displaystyle r}"></span> ialah <a href="/w/index.php?title=Pekali_korelasi_Pearson&action=edit&redlink=1" class="new" title="Pekali korelasi Pearson (laman tidak wujud)">pekali korelasi Pearson</a>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{y}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>y</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{y}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bec93eb58677e5642c86ecdb2430703a8ee57da2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:2.14ex; height:2.343ex;" alt="{\displaystyle s_{y}}"></span> ialah <a href="/wiki/Sisihan_piawai" title="Sisihan piawai">sisihan piawai</a> bagi nilai-y dan <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle s_{x}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>s</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>x</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle s_{x}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f738a5f93f694ded413a8f8da71081d0fdff4501" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.263ex; height:2.009ex;" alt="{\displaystyle s_{x}}"></span> ialah <a href="/wiki/Sisihan_piawai" title="Sisihan piawai">sisihan piawai</a> bagi nilai-x. Ini juga boleh ditulis sebagai nisbah <a href="/w/index.php?title=Kovarians&action=edit&redlink=1" class="new" title="Kovarians (laman tidak wujud)">kovarians</a>: <sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {\operatorname {cov} (Y,X)}{\operatorname {cov} (X,X)}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi>cov</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>Y</mi> <mo>,</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>cov</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mi>X</mi> <mo>,</mo> <mi>X</mi> <mo stretchy="false">)</mo> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {\operatorname {cov} (Y,X)}{\operatorname {cov} (X,X)}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1bc9cae27820f2bd0d971e8ffaaaa31d64792d3d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.671ex; width:16.201ex; height:6.509ex;" alt="{\displaystyle m={\frac {\operatorname {cov} (Y,X)}{\operatorname {cov} (X,X)}}}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="Cerun_jalan_atau_kereta_api">Cerun jalan atau kereta api</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=6" title="Sunting bahagian: Cerun jalan atau kereta api" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=6" title="Sunting kod sumber bahagian: Cerun jalan atau kereta api"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Terdapat dua cara biasa untuk menggambarkan kecuraman <a href="/wiki/Jalan_raya" title="Jalan raya">jalan</a> atau <a href="/wiki/Landasan_kereta_api" title="Landasan kereta api">jalan kereta api</a>. Satu adalah dengan sudut antara 0° dan 90° (dalam darjah), dan satu lagi dengan cerun dalam peratusan. Lihat juga <a href="/w/index.php?title=Landasan_kereta_api_gred_curam&action=edit&redlink=1" class="new" title="Landasan kereta api gred curam (laman tidak wujud)">landasan kereta api gred curam</a> dan <a href="/w/index.php?title=Landasan_kereta_api_rak&action=edit&redlink=1" class="new" title="Landasan kereta api rak (laman tidak wujud)">landasan kereta api rak</a>. </p><p>Rumus untuk menukar cerun yang diberikan sebagai peratusan kepada sudut dalam darjah dan sebaliknya ialah: </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\text{sudut}}=\arctan \left({\frac {\text{cerun}}{100\%}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>sudut</mtext> </mrow> <mo>=</mo> <mi>arctan</mi> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mtext>cerun</mtext> <mrow> <mn>100</mn> <mi mathvariant="normal">%</mi> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{sudut}}=\arctan \left({\frac {\text{cerun}}{100\%}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/53a8728f1854fc6bfbbade6b419f850945baccd9" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:25.082ex; height:6.176ex;" alt="{\displaystyle {\text{sudut}}=\arctan \left({\frac {\text{cerun}}{100\%}}\right)}"></span> (ini ialah fungsi songsang tangen; lihat <a href="/wiki/Trigonometri" title="Trigonometri">trigonometri</a> )</dd></dl> <p>dan </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mbox{cerun}}=100\%\times \tan({\mbox{sudut}}),}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>cerun</mtext> </mstyle> </mrow> <mo>=</mo> <mn>100</mn> <mi mathvariant="normal">%</mi> <mo>×</mo> <mi>tan</mi> <mo>⁡</mo> <mo stretchy="false">(</mo> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mtext>sudut</mtext> </mstyle> </mrow> <mo stretchy="false">)</mo> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mbox{cerun}}=100\%\times \tan({\mbox{sudut}}),}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/012b014239ede5ec0a32240b28360bc7d6b3ca61" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:28.438ex; height:2.843ex;" alt="{\displaystyle {\mbox{cerun}}=100\%\times \tan({\mbox{sudut}}),}"></span></dd></dl> <p>dengan <i>sudut</i> dalam darjah dan fungsi trigonometri beroperasi dalam darjah. Contohnya, cerun 100<a href="/w/index.php?title=Tanda_peratus&action=edit&redlink=1" class="new" title="Tanda peratus (laman tidak wujud)">%</a> atau 1000<a href="/wiki/Peribu" title="Peribu">‰</a> ialah sudut 45°. </p><p>Cara ketiga ialah memberikan satu unit kenaikan dalam katakan 10, 20, 50 atau 100 unit mendatar, contohnya 1:10. 1:20, 1:50 atau 1:100 (atau "1 <i>dalam</i> 10", "1 <i>dalam</i> 20", dll.) 1:10 adalah lebih curam daripada 1:20. Contohnya, kecuraman 20% bermakna 1:5 atau condong dengan sudut 11.3°. </p><p>Jalan raya dan kereta api mempunyai kedua-dua cerun membujur dan cerun silang. </p> <ul class="gallery mw-gallery-traditional"> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fail:Nederlands_verkeersbord_J6.svg" class="mw-file-description" title="Tanda amaran cerun di Belanda"><img alt="Tanda amaran cerun di Belanda" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Nederlands_verkeersbord_J6.svg/120px-Nederlands_verkeersbord_J6.svg.png" decoding="async" width="120" height="103" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/13/Nederlands_verkeersbord_J6.svg/180px-Nederlands_verkeersbord_J6.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/13/Nederlands_verkeersbord_J6.svg/240px-Nederlands_verkeersbord_J6.svg.png 2x" data-file-width="350" data-file-height="300" /></a></span></div> <div class="gallerytext">Tanda amaran cerun di <a href="/wiki/Belanda" title="Belanda">Belanda</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fail:PL_road_sign_A-23.svg" class="mw-file-description" title="Papan tanda amaran cerun di Poland"><img alt="Papan tanda amaran cerun di Poland" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/PL_road_sign_A-23.svg/120px-PL_road_sign_A-23.svg.png" decoding="async" width="120" height="106" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/PL_road_sign_A-23.svg/180px-PL_road_sign_A-23.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/PL_road_sign_A-23.svg/240px-PL_road_sign_A-23.svg.png 2x" data-file-width="513" data-file-height="453" /></a></span></div> <div class="gallerytext">Papan tanda amaran cerun di <a href="/wiki/Poland" title="Poland">Poland</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fail:Sklon%C3%ADk-kles%C3%A1n%C3%AD.jpg" class="mw-file-description" title="Jarak 1371 meter jalan kereta api dengan cerun 20‰ di Republik Czech"><img alt="Jarak 1371 meter jalan kereta api dengan cerun 20‰ di Republik Czech" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Sklon%C3%ADk-kles%C3%A1n%C3%AD.jpg/120px-Sklon%C3%ADk-kles%C3%A1n%C3%AD.jpg" decoding="async" width="120" height="90" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Sklon%C3%ADk-kles%C3%A1n%C3%AD.jpg/180px-Sklon%C3%ADk-kles%C3%A1n%C3%AD.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/5a/Sklon%C3%ADk-kles%C3%A1n%C3%AD.jpg/240px-Sklon%C3%ADk-kles%C3%A1n%C3%AD.jpg 2x" data-file-width="2048" data-file-height="1536" /></a></span></div> <div class="gallerytext">Jarak 1371 meter jalan kereta api dengan cerun 20<a href="/w/index.php?title=Per_mil&action=edit&redlink=1" class="new" title="Per mil (laman tidak wujud)">‰</a> di <a href="/wiki/Republik_Czech" title="Republik Czech">Republik Czech</a></div> </li> <li class="gallerybox" style="width: 155px"> <div class="thumb" style="width: 150px; height: 150px;"><span typeof="mw:File"><a href="/wiki/Fail:Railway_gradient_post.jpg" class="mw-file-description" title="Tiang kecerunan kereta api zaman wap menunjukkan cerun di kedua-dua arah di stesen kereta api Meols, United Kingdom"><img alt="Tiang kecerunan kereta api zaman wap menunjukkan cerun di kedua-dua arah di stesen kereta api Meols, United Kingdom" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Railway_gradient_post.jpg/120px-Railway_gradient_post.jpg" decoding="async" width="120" height="68" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/00/Railway_gradient_post.jpg/180px-Railway_gradient_post.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/00/Railway_gradient_post.jpg/240px-Railway_gradient_post.jpg 2x" data-file-width="3072" data-file-height="1728" /></a></span></div> <div class="gallerytext">Tiang kecerunan kereta api zaman wap menunjukkan cerun di kedua-dua arah di <a href="/w/index.php?title=Stesen_kereta_api_Meols&action=edit&redlink=1" class="new" title="Stesen kereta api Meols (laman tidak wujud)">stesen kereta api Meols</a>, <a href="/wiki/United_Kingdom" title="United Kingdom">United Kingdom</a></div> </li> </ul> <div class="mw-heading mw-heading2"><h2 id="Kalkulus">Kalkulus</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=7" title="Sunting bahagian: Kalkulus" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=7" title="Sunting kod sumber bahagian: Kalkulus"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-halign-right" typeof="mw:File/Frame"><a href="/wiki/Fail:Tangent_function_animation.gif" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/2/2d/Tangent_function_animation.gif" decoding="async" width="300" height="285" class="mw-file-element" data-file-width="300" data-file-height="285" /></a><figcaption> Pada setiap titik, <a href="/wiki/Terbitan" title="Terbitan">terbitan</a> ialah kecerunan <a href="/wiki/Garis_(geometri)" title="Garis (geometri)">garis</a> yang <a href="/wiki/Tangen" title="Tangen">bertangen</a> kepada <a href="/wiki/Lengkung" title="Lengkung">lengkung</a> pada titik itu. Nota: terbitan pada titik A adalah <a href="/wiki/Tanda_matematik" title="Tanda matematik">positif</a> di mana hijau dan titik sempang, <a href="/wiki/Nombor_negatif" title="Nombor negatif">negatif</a> di mana merah dan putus-putus, dan <a href="/wiki/0_(nombor)" title="0 (nombor)">sifar</a> di mana hitam dan padu.</figcaption></figure> <p>Konsep cerun adalah teras kepada <a href="/w/index.php?title=Kalkulus_pembezaan&action=edit&redlink=1" class="new" title="Kalkulus pembezaan (laman tidak wujud)">kalkulus pembezaan</a>. Untuk fungsi bukan linear, kadar perubahan berbeza di sepanjang lengkung. <a href="/wiki/Terbitan" title="Terbitan">Terbitan</a> bagi fungsi pada satu titik ialah kecerunan garis <a href="/wiki/Tangen" title="Tangen">tangen</a> kepada lengkung pada titik itu, dan dengan itu sama dengan kadar perubahan fungsi pada titik itu. </p><p>Jika kita biarkan Δ<i>x</i> dan Δ<i>y</i> ialah jarak (masing-masing sepanjang paksi <i>x</i> dan <i>y</i>) antara dua titik pada lengkung, maka cerun yang diberikan oleh takrif di atas, </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle m={\frac {\Delta y}{\Delta x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>m</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle m={\frac {\Delta y}{\Delta x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5a20d2a034e0b9063b50df5ce9876dd5b9734162" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:9.241ex; height:5.676ex;" alt="{\displaystyle m={\frac {\Delta y}{\Delta x}}}"></span> ,</dd></dl> <p>ialah kecerunan <a href="/w/index.php?title=Garis_sekan&action=edit&redlink=1" class="new" title="Garis sekan (laman tidak wujud)">garis sekan</a> pada lengkung. Untuk garis, sekan di antara mana-mana dua titik ialah garis itu sendiri, tetapi ini tidak berlaku untuk mana-mana jenis lengkung lain. </p><p>Dengan menggerakkan dua titik lebih rapat supaya Δ<i>y</i> dan Δ<i>x</i> berkurangan, garis sekan lebih hampir menghampiri garis tangen ke lengkung, dan oleh itu kecerunan sekan menghampiri tangen. Dengan menggunakan <a href="/w/index.php?title=Kalkulus_pembezaan&action=edit&redlink=1" class="new" title="Kalkulus pembezaan (laman tidak wujud)">kalkulus pembezaan</a>, kita boleh menentukan <a href="/wiki/Had_fungsi" title="Had fungsi">had</a>, atau nilai yang Δ<i>y</i>/Δ<i>x</i> menghampiri apabila Δ<i>y</i> dan Δ<i>x</i> semakin menghampiri <a href="/wiki/0_(nombor)" title="0 (nombor)">sifar</a>; ia berikutan bahawa had ini ialah cerun tepat tangen. Jika <i>y</i> bergantung kepada <i>x</i>, maka sudah memadai untuk mengambil had di mana hanya Δ<i>x</i> menghampiri sifar. Oleh itu, kecerunan tangen ialah had Δ<i>y</i>/Δ<i>x</i> apabila Δ<i>x</i> menghampiri sifar, atau d<i>y</i>/d<i>x</i>. Kita memanggil had ini <a href="/wiki/Terbitan" title="Terbitan">terbitan</a>. </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\frac {\mathrm {d} y}{\mathrm {d} x}}=\lim _{\Delta x\to 0}{\frac {\Delta y}{\Delta x}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>y</mi> </mrow> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>x</mi> </mrow> </mfrac> </mrow> <mo>=</mo> <munder> <mo movablelimits="true" form="prefix">lim</mo> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">Δ</mi> <mi>x</mi> <mo stretchy="false">→</mo> <mn>0</mn> </mrow> </munder> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mi mathvariant="normal">Δ</mi> <mi>y</mi> </mrow> <mrow> <mi mathvariant="normal">Δ</mi> <mi>x</mi> </mrow> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\frac {\mathrm {d} y}{\mathrm {d} x}}=\lim _{\Delta x\to 0}{\frac {\Delta y}{\Delta x}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/5acd8221e8accfd75cb6304f98a66bcfee1f518d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.171ex; width:15.82ex; height:5.843ex;" alt="{\displaystyle {\frac {\mathrm {d} y}{\mathrm {d} x}}=\lim _{\Delta x\to 0}{\frac {\Delta y}{\Delta x}}}"></span></dd></dl> <p>Nilainya pada satu titik pada fungsi memberikan kita cerun tangen pada titik itu. Sebagai contoh, biarkan <i>y</i> = <i>x</i><sup>2</sup>. Satu titik pada fungsi ini ialah (−2,4). Terbitan bagi fungsi ini ialah <span class="nowrap"><span class="frac nowrap"><sup>d<i>y</i></sup>⁄<sub>d<i>x</i></sub></span> = 2<i>x</i></span>. Jadi kecerunan garis tangen kepada y pada (−2,4) ialah 2 ⋅ (−2) = −4. Persamaan garis tangen ini ialah: y − 4 = (−4)(x − (−2)) atau y = −4x − 4. </p> <div class="mw-heading mw-heading2"><h2 id="Lihat_juga">Lihat juga</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=8" title="Sunting bahagian: Lihat juga" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=8" title="Sunting kod sumber bahagian: Lihat juga"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/w/index.php?title=Jarak_Euclid&action=edit&redlink=1" class="new" title="Jarak Euclid (laman tidak wujud)">Jarak Euclid</a></li> <li><a href="/w/index.php?title=Gred_(curam)&action=edit&redlink=1" class="new" title="Gred (curam) (laman tidak wujud)">Gred</a></li> <li><a href="/wiki/Satah_condong" title="Satah condong">Satah condong</a></li> <li><a href="/wiki/Fungsi_linear" title="Fungsi linear">Fungsi linear</a></li> <li><a href="/w/index.php?title=Garis_cerun_terbesar&action=edit&redlink=1" class="new" title="Garis cerun terbesar (laman tidak wujud)">Garis cerun terbesar</a></li> <li><a href="/w/index.php?title=Takrifan_cerun&action=edit&redlink=1" class="new" title="Takrifan cerun (laman tidak wujud)">Takrifan cerun</a></li> <li><a href="/w/index.php?title=Penganggar_Theil%E2%80%93Sen&action=edit&redlink=1" class="new" title="Penganggar Theil–Sen (laman tidak wujud)">Penganggar Theil–Sen</a>, garis dengan cerun <a href="/wiki/Median" title="Median">median</a> di antara set titik sampel</li></ul> <div class="mw-heading mw-heading2"><h2 id="Rujukan">Rujukan</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Cerun&veaction=edit&section=9" title="Sunting bahagian: Rujukan" class="mw-editsection-visualeditor"><span>sunting</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Cerun&action=edit&section=9" title="Sunting kod sumber bahagian: Rujukan"><span>sunting sumber</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r6173370">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r5110723">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFClaphamNicholson2009" class="citation web cs1">Clapham, C.; Nicholson, J. (2009). <a rel="nofollow" class="external text" href="https://web.archive.org/web/20131029203826/http://web.cortland.edu/matresearch/OxfordDictionaryMathematics.pdf">"Oxford Concise Dictionary of Mathematics, Gradient"</a> <span class="cs1-format">(PDF)</span>. Addison-Wesley. m/s. 348. Diarkibkan daripada <a rel="nofollow" class="external text" href="http://web.cortland.edu/matresearch/OxfordDictionaryMathematics.pdf">yang asal</a> <span class="cs1-format">(PDF)</span> pada 29 October 2013<span class="reference-accessdate">. Dicapai pada <span class="nowrap">1 September</span> 2013</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Oxford+Concise+Dictionary+of+Mathematics%2C+Gradient&rft.pages=348&rft.pub=Addison-Wesley&rft.date=2009&rft.aulast=Clapham&rft.aufirst=C.&rft.au=Nicholson%2C+J.&rft_id=http%3A%2F%2Fweb.cortland.edu%2Fmatresearch%2FOxfordDictionaryMathematics.pdf&rfr_id=info%3Asid%2Fms.wikipedia.org%3ACerun" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5110723"><cite id="CITEREFO'Brien1844" class="citation cs2">O'Brien, M. 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(1888), <i>Treatise on Plane Co-Ordinate Geometry as Applied to the Straight Line and Conic Sections</i>, London: Macmillan</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Treatise+on+Plane+Co-Ordinate+Geometry+as+Applied+to+the+Straight+Line+and+Conic+Sections&rft.place=London&rft.pub=Macmillan&rft.date=1888&rft.aulast=Todhunter&rft.aufirst=I.&rfr_id=info%3Asid%2Fms.wikipedia.org%3ACerun" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5110723"><cite id="CITEREFWeisstein" class="citation web cs1">Weisstein, Eric W. <a rel="nofollow" class="external text" href="http://mathworld.wolfram.com/Slope.html">"Slope"</a>. MathWorld--A Wolfram Web Resource. <a rel="nofollow" class="external text" href="https://web.archive.org/web/20161206182915/http://mathworld.wolfram.com/Slope.html">Diarkibkan</a> daripada yang asal pada 6 December 2016<span class="reference-accessdate">. Dicapai pada <span class="nowrap">30 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Slope&rft.pub=MathWorld--A+Wolfram+Web+Resource&rft.aulast=Weisstein&rft.aufirst=Eric+W.&rft_id=http%3A%2F%2Fmathworld.wolfram.com%2FSlope.html&rfr_id=info%3Asid%2Fms.wikipedia.org%3ACerun" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r5110723"><cite class="citation book cs1"><i>Further Mathematics Units 3&4 VCE (Revised)</i>. 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Math Open Reference. 2009<span class="reference-accessdate">. Dicapai pada <span class="nowrap">30 October</span> 2016</span>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=unknown&rft.btitle=Slope+of+a+Line+%28Coordinate+Geometry%29&rft.pub=Math+Open+Reference&rft.date=2009&rft_id=http%3A%2F%2Fwww.mathopenref.com%2Fcoordslope.html&rfr_id=info%3Asid%2Fms.wikipedia.org%3ACerun" class="Z3988"></span> interactive</li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Diambil daripada "<a dir="ltr" href="https://ms.wikipedia.org/w/index.php?title=Cerun&oldid=5843404">https://ms.wikipedia.org/w/index.php?title=Cerun&oldid=5843404</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Khas:Kategori" title="Khas:Kategori">Kategori</a>: <ul><li><a href="/wiki/Kategori:Nisbah" title="Kategori:Nisbah">Nisbah</a></li><li><a href="/wiki/Kategori:Matematik_asas" title="Kategori:Matematik asas">Matematik asas</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Kategori-kategori tersembunyi: <ul><li><a href="/wiki/Kategori:Rencana_yang_mengandungi_teks_bahasa_secara_jelas_menyebut_bahasa_Melayu_(bahasa_makro)" title="Kategori:Rencana yang mengandungi teks bahasa secara jelas menyebut bahasa Melayu (bahasa makro)">Rencana yang mengandungi teks bahasa secara jelas menyebut bahasa Melayu (bahasa makro)</a></li><li><a href="/wiki/Kategori:Lang_and_lang-xx_using_deprecated_ISO_639_codes" title="Kategori:Lang and lang-xx using deprecated ISO 639 codes">Lang and lang-xx using deprecated ISO 639 codes</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> Laman ini kali terakhir disunting pada 04:05, 16 Mei 2023.</li> <li id="footer-info-copyright">Teks disediakan di bawah <a rel="nofollow" class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.ms">Lesen Creative Commons Pengiktirafan/Perkongsian Serupa</a>; terma tambahan mungkin digunapakai. 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