{"id":319,"date":"2022-04-13T09:02:39","date_gmt":"2022-04-13T09:02:39","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=319"},"modified":"2025-08-20T01:38:17","modified_gmt":"2025-08-20T01:38:17","slug":"t-11-linear-equations-solve-for-y","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-11-linear-equations-solve-for-y\/","title":{"rendered":"T.11 Linear equations: solve for y"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong> Linear equations: solve for y<\/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\/DAGwHrvp-m8\/__TJpxkiMC1T1q4v-4FY3Q\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwHrvp-m8&#x2F;__TJpxkiMC1T1q4v-4FY3Q&#x2F;watch?utm_content=DAGwHrvp-m8&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.11 Linear equations: solve for y<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key Notes :<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-c2037ec6abfb4608cbd1b738a29dce61\" style=\"color:#000060\"><strong> What is a Linear Equation?<\/strong><\/p>\n\n\n\n<p>A <strong>linear equation<\/strong> is an equation in which:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Variables have <strong>power 1<\/strong><\/li>\n\n\n\n<li>Graph is a <strong>straight line<\/strong><\/li>\n\n\n\n<li>Can be written in the standard form:<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading alignwide has-text-align-center has-normal-font-size\"><strong>ax+by=c<\/strong><\/h2>\n\n\n\n<p>where a,b,c are numbers, x and y are variables.<\/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-7308867c51cc81127166232bf528765e\" style=\"color:#000060\"><strong> Why Solve for y?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To rewrite in <strong>slope-intercept form<\/strong>:<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading has-text-align-center has-normal-font-size\"><strong>y=mx+b<\/strong><\/h2>\n\n\n\n<p>where:<br><strong>m<\/strong> = slope (rate of change)<br><strong>b<\/strong> = y-intercept (where the line crosses y-axis)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Makes <strong>graphing<\/strong> 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-c38f779956d74bdeb61400929bbcaa0a\" style=\"color:#000060\"><strong> General Steps to Solve for y<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list has-normal-font-size\">\n<li><strong>Find<\/strong> the term containing y.<\/li>\n\n\n\n<li><strong>Move<\/strong> all other terms to the opposite side (+ becomes \u2212, \u2212 becomes +).<\/li>\n\n\n\n<li><strong>Divide<\/strong> by the coefficient of y to make it y= \u2026.<\/li>\n\n\n\n<li><strong>Simplify<\/strong> fractions or negatives if needed.<\/li>\n<\/ul>\n\n\n\n<p>\ud83d\udca1 <strong>Think-Check:<\/strong> The yyy must be <strong>alone<\/strong> on one side, with coefficient 1.<\/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-62895b0aed53a3bee3fd762c9a006cc0\" style=\"color:#000060\"><strong> Worked Examples<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-8e468028c114965a7d30ec3a60203681\" style=\"color:#000060\"><strong>Example 1<\/strong> \u2013 Easy<\/h4>\n\n\n\n<p>Solve for yyy:<\/p>\n\n\n\n<p class=\"has-text-align-center\">3x+y=7<\/p>\n\n\n\n<p>Step 1: Move 3x:<\/p>\n\n\n\n<p class=\"has-text-align-center\">y=\u22123x+7<\/p>\n\n\n\n<p>\u2705 <strong>Check:<\/strong> y alone, in slope-intercept form.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-d4fb66c559067b9609f54fa70069b540\" style=\"color:#000060\"><strong>Example 2<\/strong> \u2013 Needs Division<\/h4>\n\n\n\n<p>Solve for y: <\/p>\n\n\n\n<p class=\"has-text-align-center\">2x\u22124y=8<\/p>\n\n\n\n<p>Step 1: Move 2x: <\/p>\n\n\n\n<p class=\"has-text-align-center\">\u22124y=\u22122x+8<\/p>\n\n\n\n<p>Step 2: Divide by \u22124:\u200b <\/p>\n\n\n\n<p class=\"has-text-align-center\">y=\u22122x+8\u200b\/\u22124<\/p>\n\n\n\n<p>Step 3: Simplify:<\/p>\n\n\n\n<p class=\"has-text-align-center\">y=x\/2\u22122<\/p>\n\n\n\n<p>\u2705 <strong>Check:<\/strong> slope = 1\/2, intercept = \u22122.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-c21e3e53fb658a875ef98aad1d667b1f\" style=\"color:#000020\"><strong>Example 3<\/strong> \u2013 Negative y term<\/h4>\n\n\n\n<p>Solve for y:<\/p>\n\n\n\n<p class=\"has-text-align-center\">\u2212y+4x=8<\/p>\n\n\n\n<p>Step 1: Move 4x <\/p>\n\n\n\n<p class=\"has-text-align-center\">\u2212y=\u22124x+8<\/p>\n\n\n\n<p>Step 2: Multiply by -1:<\/p>\n\n\n\n<p class=\"has-text-align-center\"> y=4x\u22128<\/p>\n\n\n\n<p>\u2705 <strong>Check:<\/strong> slope = 4, intercept = \u22128.<\/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-92628219530804be47680b02cce6b2b9\" style=\"color:#000060\"><strong>Common Mistakes to Avoid<\/strong><\/h3>\n\n\n\n<p>\u274c Forgetting to change the sign when moving a term.<br>\u274c Not dividing all terms when removing a coefficient.<br>\u274c Mixing up slope (m) and intercept (b).<\/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-887398d43e7e5fa5eb692b3f53a0e7a3\" style=\"color:#000060\"><strong> Quick Practice<\/strong> \u2013 Solve for y<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>4x+y=10<\/li>\n\n\n\n<li>5x\u22122y=6<\/li>\n\n\n\n<li>7y+3x=14<\/li>\n\n\n\n<li>\u2212y+2x=\u22125<\/li>\n\n\n\n<li>6y\u2212x=126<\/li>\n<\/ol>\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-ed32886cc4ed0fccc087fbe67ef2411f\" style=\"color:#000060\"><strong> Challenge Question<\/strong><\/h3>\n\n\n\n<p>If 3x\u22122y=6, write it in slope-intercept form and <strong>identify slope and y-intercept<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<p class=\"has-text-align-center has-text-color has-large-font-size\" style=\"color:#105000\"><strong>Learn with an example<\/strong><\/p>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#8eddd5\"><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>Rewrite the following equation in slope-intercept form.<\/p>\n\n\n\n<p>y-1=1\/2(x-10)<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Write your answer using integers, proper fractions, and improper fractions in simplest form<em>.<\/em>_________<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Rewrite the equation in&nbsp;slope-intercept&nbsp;form. <\/p>\n\n\n\n<p><em>y<\/em>&nbsp;\u2212 1&nbsp;=&nbsp;1\/2(<em>x<\/em>&nbsp;\u2212 10)<\/p>\n\n\n\n<p>y&nbsp;\u2212 1&nbsp;=&nbsp;1\/2x&nbsp;\u2212 5      Apply the distributive property<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;1\/2<em>x<\/em>&nbsp;\u2212 4         Add 1 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:#64c3d6\"><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>Rewrite the following equation in slope-intercept form.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;\u2212 10 =&nbsp;-10(<em>x<\/em>&nbsp;+ 2)<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Write your answer using integers, proper fractions, and improper fractions in simplest form.______<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Rewrite the equation in&nbsp;slope-intercept&nbsp;form.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;\u2212 10&nbsp;=-10(<em>x<\/em>&nbsp;+ 2)<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;\u2212 10&nbsp;=&nbsp;-10<em>x<\/em>&nbsp;\u2212 20     Apply the distributive property<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;<sup>\u2013<\/sup>10<em>x<\/em>&nbsp;\u2212 10        Add 10 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:#e3abdf\"><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>Rewrite the following equation in slope-intercept form.<\/p>\n\n\n\n<p>y-7=1\/2(x+6)<\/p>\n\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Write your answer using integers, proper fractions, and improper fractions in simplest form_______<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>Rewrite the equation in&nbsp;slope-intercept&nbsp;form.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;\u2212 7&nbsp;=&nbsp;1\/2(<em>x<\/em>&nbsp;+ 6)<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;\u2212 7&nbsp;=&nbsp;1\/2<em>x<\/em>&nbsp;+ 3      Apply the distributive property<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;1\/2<em>x<\/em>&nbsp;+ 10       Add 7 to both sides<\/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\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\/78187\/774\/163\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-121.png\" alt=\"\" class=\"wp-image-8063\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-121.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-121-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-121-150x150.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\/76987\/778\/432\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-130.png\" alt=\"\" class=\"wp-image-8064\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-130.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-130-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-130-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Linear equations: solve for y T.11 Linear equations: solve for y by Delta publications Key Notes : What is a Linear Equation? A linear equation is an equation in which: ax+by=c where a,b,c are numbers, x and y are variables. Why Solve for y? y=mx+b where:m = slope (rate of change)b = y-intercept (where the<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-11-linear-equations-solve-for-y\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.11 Linear equations: solve for y&#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-319","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/319","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=319"}],"version-history":[{"count":22,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/319\/revisions"}],"predecessor-version":[{"id":17551,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/319\/revisions\/17551"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=319"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}