{"id":325,"date":"2022-04-13T09:03:33","date_gmt":"2022-04-13T09:03:33","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=325"},"modified":"2025-08-20T01:41:12","modified_gmt":"2025-08-20T01:41:12","slug":"t-14-write-equations-in-standard-form","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-14-write-equations-in-standard-form\/","title":{"rendered":"T.14 Write equations in standard form"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#00056d;text-transform:uppercase\"><strong>Write equations in standard form<\/strong><\/h2>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\" style=\"flex-basis:100%\">\n<div style=\"position: relative; width: 100%; height: 0; padding-top: 56.2500%;\n padding-bottom: 0; box-shadow: 0 2px 8px 0 rgba(63,69,81,0.16); margin-top: 1.6em; margin-bottom: 0.9em; overflow: hidden;\n border-radius: 8px; will-change: transform;\">\n  <iframe loading=\"lazy\" style=\"position: absolute; width: 100%; height: 100%; top: 0; left: 0; border: none; padding: 0;margin: 0;\"\n    src=\"https:\/\/www.canva.com\/design\/DAGwHpHkVb8\/waqqI9GoUA46ka3hIa64gA\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwHpHkVb8&#x2F;waqqI9GoUA46ka3hIa64gA&#x2F;watch?utm_content=DAGwHpHkVb8&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.14 Write equations in standard form<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-04d9d6410ea0aa79bd5fd62d138d8458\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-b2a1e6536a4529147a5d0ec5edd43c1c\" style=\"color:#000060\"><strong> What is Standard Form?<\/strong><\/h3>\n\n\n\n<p>A linear equation in <strong>Standard Form<\/strong> is written as: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Ax+By=C<\/strong><\/p>\n\n\n\n<p>where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A, B and C are integers<\/li>\n\n\n\n<li>A should be <strong>non-negative<\/strong> (A \u2265 0)<\/li>\n\n\n\n<li>x and y are variables<\/li>\n\n\n\n<li>No fractions or decimals are allowed<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-7f33e1ff6a0a91550689167b9584ceed\" style=\"color:#000060\"><strong> Why Use Standard Form?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Useful for <strong>finding intercepts<\/strong> quickly<\/li>\n\n\n\n<li>Common in <strong>word problems<\/strong> and real-life situations<\/li>\n\n\n\n<li>Makes comparing equations easier<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-262a7565a2e69bb922231660e60233e2\" style=\"color:#000060\"><strong>Converting from Slope-Intercept Form to Standard Form<\/strong><\/h3>\n\n\n\n<p><strong>Slope-Intercept Form:<\/strong> <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>y=mx+b<\/strong><\/p>\n\n\n\n<p><strong>Steps:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Move the x-term to the left side (so both x and y are on the same side).<\/li>\n\n\n\n<li>Remove fractions or decimals by multiplying through by the denominator.<\/li>\n\n\n\n<li>Make sure A\u22650 and all coefficients are integers.<\/li>\n<\/ol>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Example 1<\/strong><br>Convert y=2x+3 to standard form:<br>Step 1: Move 2x to left: <\/p>\n\n\n\n<p class=\"has-text-align-center\">\u22122x+y=3<\/p>\n\n\n\n<p>Step 2: Multiply by -1 (to make A&gt;0): <\/p>\n\n\n\n<p class=\"has-text-align-center\">2x\u2212y=\u22123<\/p>\n\n\n\n<p>\u2705 Standard Form: <\/p>\n\n\n\n<p class=\"has-text-align-center\">2x\u2212y=\u22123<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p><strong>Example 2<\/strong><br>Convert y=3\/4x\u22122 to standard form:<br>Step 1: Move 3\/4x to left:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\u22123\/4x+y=\u22122<\/p>\n\n\n\n<p>Step 2: Multiply all terms by 4 to clear fraction: <\/p>\n\n\n\n<p class=\"has-text-align-center\">\u22123x+4y=\u22128<\/p>\n\n\n\n<p>Step 3: Multiply by -1:<\/p>\n\n\n\n<p class=\"has-text-align-center\"> 3x\u22124y=8<\/p>\n\n\n\n<p>\u2705 Standard Form: 3x\u22124y=8<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-cd520e69868a3a33f4d69dcaede262f9\" style=\"color:#000060\"><strong> From Point-Slope Form to Standard Form<\/strong><\/h3>\n\n\n\n<p>Point-Slope Form:<\/p>\n\n\n\n<p class=\"has-text-align-center\"> y\u2212y<sub>1<\/sub>=m(x\u2212x<sub>1<\/sub>)<\/p>\n\n\n\n<p>Expand, simplify, and arrange into <strong>Ax+By=C<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-472667ca196286a8c9a765a00fef1177\" style=\"color:#000060\"><strong> Key Rules for Standard Form<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A, B, C are integers (no fractions\/decimals)<\/li>\n\n\n\n<li>A\u2265 0<\/li>\n\n\n\n<li>Write x first, then y, then constant<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color wp-elements-96e3aaf0dbb8be9d2a91644613bed519\" style=\"color:#000060\"><strong> Practice Problems<\/strong><\/h3>\n\n\n\n<p>Convert to standard form:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>y=\u22123x+7<\/li>\n\n\n\n<li>y=2\/5x+4<\/li>\n\n\n\n<li>y\u22123=5(x\u22122)<\/li>\n\n\n\n<li>y=0.5x\u22126<\/li>\n<\/ol>\n\n\n\n<p class=\"has-text-align-center has-text-color has-link-color has-large-font-size wp-elements-3fefd20f8ce119a518e5f53333ab5486\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#a6d8f2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-7a382d1eba93c05716fe00800da139e1\" style=\"color:#b00012\">Rewrite the following equation in standard form.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\">y= \u201310\/7 x \u2212 10<\/p>\n<\/div><\/div>\n\n\n\n<p>Rewrite the equation in standard form.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;-10\/7 <em>x<\/em>&nbsp;\u2212 10<br>10\/7x&nbsp;+&nbsp;y&nbsp;=&nbsp;-10          [ add 10\/7 x to both sides ]<\/p>\n\n\n\n<p>10x&nbsp;+ 7y&nbsp;=&nbsp;-70           [ Multiply both sides by 7 ]<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#f2a6f2\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-7a382d1eba93c05716fe00800da139e1\" style=\"color:#b00012\">Rewrite the following equation in standard form.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\"><em>y<\/em>&nbsp;=&nbsp;-2<em>x<\/em>&nbsp;\u2212 3<\/p>\n<\/div><\/div>\n\n\n\n<p>Rewrite the equation in standard form.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;-2<em>x<\/em>&nbsp;\u2212 3<br>2x&nbsp;+&nbsp;y&nbsp;=&nbsp;-3       Add 2x to both sides<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b3a2eb\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-text-color has-link-color wp-elements-7a382d1eba93c05716fe00800da139e1\" style=\"color:#b00012\">Rewrite the following equation in standard form.<\/p>\n\n\n\n<p class=\"has-text-align-center has-normal-font-size\"><em>y<\/em>&nbsp;= 2<em>x<\/em>&nbsp;+ 10<\/p>\n<\/div><\/div>\n\n\n\n<p>Rewrite the equation in standard form.<\/p>\n\n\n\n<p>y = 2x + 10<\/p>\n\n\n\n<p>\u20132x + y = 10     Subtract 2x from both sides<\/p>\n\n\n\n<p>2x \u2212 y = \u201310     Multiply both sides by \u20131<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color has-large-font-size\" style=\"color:#d90000\">Let&#8217;s Practice!<\/p>\n<\/div><\/div>\n\n\n\n<hr class=\"wp-block-separator has-css-opacity\"\/>\n\n\n\n<div class=\"wp-block-columns is-layout-flex wp-container-core-columns-is-layout-9d6595d7 wp-block-columns-is-layout-flex\">\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78191\/656\/429\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-118.png\" alt=\"\" class=\"wp-image-8054\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-118.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-118-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-118-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n\n\n\n<div class=\"wp-block-column is-layout-flow wp-block-column-is-layout-flow\">\n<figure class=\"wp-block-image size-full\"><a href=\"https:\/\/wordwall.net\/play\/78261\/243\/138\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-127.png\" alt=\"\" class=\"wp-image-8055\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-127.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-127-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-127-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Write equations in standard form T.14 Write equations in standard form by Delta publications key notes: What is Standard Form? A linear equation in Standard Form is written as: Ax+By=C where: Why Use Standard Form? Converting from Slope-Intercept Form to Standard Form Slope-Intercept Form: y=mx+b Steps: Example 1Convert y=2x+3 to standard form:Step 1: Move 2x<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-14-write-equations-in-standard-form\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.14 Write equations in standard form&#8221;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-325","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/325","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/comments?post=325"}],"version-history":[{"count":18,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/325\/revisions"}],"predecessor-version":[{"id":17554,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/325\/revisions\/17554"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=325"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}