{"id":329,"date":"2022-04-13T09:04:08","date_gmt":"2022-04-13T09:04:08","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=329"},"modified":"2025-08-20T01:43:12","modified_gmt":"2025-08-20T01:43:12","slug":"t-16-standard-form-graph-an-equation","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-16-standard-form-graph-an-equation\/","title":{"rendered":"T.16 Standard form: graph an equation"},"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>Standard form: graph an equation<\/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\/DAGwH60cU6I\/QRh9J286l8eVqt8MJaOZyw\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwH60cU6I&#x2F;QRh9J286l8eVqt8MJaOZyw&#x2F;watch?utm_content=DAGwH60cU6I&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.16 Standard form: graph an equation<\/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<p class=\"has-text-color has-large-font-size\" style=\"color:#000060\"><strong> Standard Form Reminder<\/strong><\/p>\n\n\n\n<p>A linear equation in standard form looks like this: <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Ax+By=C<\/strong><\/p>\n\n\n\n<p>where A, B, and C are integers (no fractions), and x,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-f2a8733a974f4451821b9dd888368c2b\" style=\"color:#000060\"><strong> Why Use Intercepts to Graph?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Easy and fast method<\/li>\n\n\n\n<li>Just find where the line crosses the axes<\/li>\n\n\n\n<li>Only need <strong>two points<\/strong> to draw the whole line!<\/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-2abcd548691eb08ae4d8748cfce57c74\" style=\"color:#000060\"><strong> Step-by-Step Guide to Graph Using Intercepts<\/strong><\/h3>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>Step<\/th><th>What to do<\/th><th>How to do it<\/th><th>Result<\/th><\/tr><\/thead><tbody><tr><td><strong>1<\/strong><\/td><td>Find <strong>x-intercept<\/strong><\/td><td>Set y=0 in Ax+By=C solve for x<\/td><td>Point (x,0)<\/td><\/tr><tr><td><strong>2<\/strong><\/td><td>Find <strong>y-intercept<\/strong><\/td><td>Set x=0 in Ax+By=C, solve for y<\/td><td>Point (0,y)<\/td><\/tr><tr><td><strong>3<\/strong><\/td><td>Plot both points<\/td><td>Mark (x,0)) and (0,y) on graph paper<\/td><td>Visual points<\/td><\/tr><tr><td><strong>4<\/strong><\/td><td>Draw the line<\/td><td>Use a ruler to connect points<\/td><td>Straight line graph<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading has-large-font-size\"><strong> Example: Graph 2x+3y=12<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Find x-intercept:<\/strong><br>Set y=0<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">2x=12\u2005\u200a\u27f9\u2005\u200ax=6<\/p>\n\n\n\n<p>Point: (6,0)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Find y-intercept:<\/strong><br>Set x=0<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\">3y=12\u2005\u200a\u27f9\u2005\u200ay=4<\/p>\n\n\n\n<p>Point: (0,4)<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Plot points (6,0) and (0,4) on the graph paper.<\/strong><\/li>\n\n\n\n<li><strong>Draw a straight line through them.<\/strong><\/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-6df49384a555c7dbe08d40e0a9185dd6\" style=\"color:#000060\"><strong> Tips for Success<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always check <strong>both intercepts<\/strong> before plotting.<\/li>\n\n\n\n<li>If intercepts are fractions, multiply the whole equation by the denominator to clear them.<\/li>\n\n\n\n<li>When A=0 or B=0 the line is either <strong>horizontal<\/strong> or <strong>vertical<\/strong>:<\/li>\n\n\n\n<li>If A=0, equation is By=C \u2192 horizontal line y=C\/B.<\/li>\n\n\n\n<li>If B=0, equation is Ax=C\u2192 vertical line x=C\/A.<\/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-54f11fabf8c90f531aba8ae186c76cb4\" style=\"color:#000020\"><strong>Practice<\/strong><\/h3>\n\n\n\n<p>Graph these equations:<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-normal-font-size\">1.  3x+4y=12<\/p>\n\n\n\n<p>2.  5x\u22122y=10<\/p>\n\n\n\n<p>3.  x+y=7<\/p>\n\n\n\n<p>4.  6x=18<\/p>\n\n\n\n<p class=\"has-primary-color has-text-color has-normal-font-size\">5.  4y=8<\/p>\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 has-background has-normal-font-size\" style=\"background-color:#94ede7\"><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-large-font-size\"><strong>Graph&nbsp;this line using&nbsp;intercepts: <\/strong><\/p>\n\n\n\n<p class=\"has-text-align-center has-text-color has-normal-font-size\" style=\"color:#8c0000\"><strong> 2x+3y = 6<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p><strong>Step 1:&nbsp;Find the&nbsp;<\/strong>x-intercept.<\/p>\n\n\n\n<p>The&nbsp;x-intercept&nbsp;is on the&nbsp;x-axis,&nbsp;where&nbsp;y=0.&nbsp;Plug&nbsp;y=0&nbsp;into the equation and solve for the&nbsp;x-intercept&nbsp;x.<\/p>\n\n\n\n<p>2x+3y=6<\/p>\n\n\n\n<p>2x+3(0)=6     Plugin&nbsp;y=0<\/p>\n\n\n\n<p>2x=6 <\/p>\n\n\n\n<p>x=3<\/p>\n\n\n\n<p>The&nbsp;x-intercept&nbsp;is&nbsp;3.&nbsp;Its coordinates are&nbsp;(3,0).<\/p>\n\n\n\n<p><strong>Step 2:&nbsp;Find the&nbsp;<\/strong>y-intercept.<\/p>\n\n\n\n<p>The&nbsp;y-intercept&nbsp;is on the&nbsp;y-axis,&nbsp;where&nbsp;x=0.&nbsp;Plug&nbsp;x=0&nbsp;into the equation and solve for the&nbsp;y-intercept&nbsp;y.<\/p>\n\n\n\n<p>2x+3y=6<\/p>\n\n\n\n<p>2(0)+3y=6    Plug&nbsp;in&nbsp;x=0<\/p>\n\n\n\n<p>3y=6<\/p>\n\n\n\n<p>y=2<\/p>\n\n\n\n<p>The&nbsp;y-intercept&nbsp;is&nbsp;2.&nbsp;Its coordinates are&nbsp;(0,2).<\/p>\n\n\n\n<p><strong>Step&nbsp;3: Use the intercepts to&nbsp;graph.<\/strong><\/p>\n\n\n\n<p>Plot&nbsp;the&nbsp;x-intercept&nbsp;(3,0)&nbsp;and the&nbsp;y-intercept&nbsp;(0,2).&nbsp;The graph is the straight line connecting&nbsp;them.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-23.png\" alt=\"\" class=\"wp-image-11610\" style=\"width:410px;height:auto\"\/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#a0ea9b\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p class=\"has-foreground-color has-text-color has-link-color wp-elements-9817014ca16160a39529e16a495e9bb6\">Graph this line using intercepts:<br>8x\u20137y=56<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-31ce257d208edcb0bd8cf2e3d098e5d2\" style=\"color:#b00012\"><br>Click to select points on the graph.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24.png\" alt=\"\" class=\"wp-image-11612\" style=\"width:368px;height:auto\"\/><\/figure><\/div><\/div><\/div>\n\n\n\n<p><strong>Step 1: Find the x-intercept.<\/strong><br>The x-intercept is on the x-axis, where y=0. Plug y=0 into the equation and solve for the x-intercept x.<br>8x\u20137y= 56<br>8x\u20137(0) = 56 Plug in y=0<br>8x = 56 Simplify<br>x= 7 Divide both sides by 8<br>The x-intercept is 7. Its coordinates are (7,0).<br><strong>Step 2: Find the y-intercept.<\/strong><br>The y-intercept is on the y-axis, where x=0. Plug x=0 into the equation and solve for the y-intercept y.<br>8x\u20137y = 56<br>8(0)\u20137y = 56    Plugin x=0<br>\u20137y = 56         Simplify<\/p>\n\n\n\n<p>y\u20138                Divide both sides by \u20137 <\/p>\n\n\n\n<p>The y-intercept is\u20138 Its coordinates are (0,\u20138).<br><strong>Step 3: Use the intercepts to graph.<\/strong><br>Plot the x-intercept (7,0) and the y-intercept (0, \u20138). The graph is the straight line connecting them.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-25.png\" alt=\"\" class=\"wp-image-11613\" style=\"width:410px;height:auto\"\/><\/figure><\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#b78de7\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background-background-color has-background\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Graph this line using intercepts:<br>2x+5y=\u201310<\/p>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-31ce257d208edcb0bd8cf2e3d098e5d2\" style=\"color:#b00012\"><br>Click to select points on the graph.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-24-1.png\" alt=\"\" class=\"wp-image-11614\" style=\"width:362px;height:auto\"\/><\/figure><\/div><\/div><\/div>\n\n\n\n<p><strong>Step 1: Find the x-intercept.<\/strong><br>The x-intercept is on the x-axis, where y=0. Plug y=0 into the equation and solve for the x-intercept x.<\/p>\n\n\n\n<p>2x+5y=\u201310<\/p>\n\n\n\n<p>2x+5(0)=\u201310 Plugin y=0<\/p>\n\n\n\n<p>2x\u201310 Simplify<\/p>\n\n\n\n<p>x\u20135 Divide both sides by 2<\/p>\n\n\n\n<p>The x-intercept is \u20135. Its coordinates are (\u20135,0).<\/p>\n\n\n\n<p><strong>Step 2: Find the y-intercept.<\/strong><br>The y-intercept is on the y-axis, where x=0. Plug x=0 into the equation and solve for the y-intercept y.<\/p>\n\n\n\n<p>2x+5y=\u201310<\/p>\n\n\n\n<p>2(0)+5y=\u201310 Plugin x=0<\/p>\n\n\n\n<p>5y\u201310 Simplify<\/p>\n\n\n\n<p>y\u20132 Divide both sides by 5<\/p>\n\n\n\n<p>The y-intercept is\u20132 Its coordinates are (0,\u20132).<\/p>\n\n\n\n<p><strong>Step 3: Use the intercepts to graph<\/strong>.<br>Plot the x-intercept (\u20135,0) and the y-intercept (0,\u20132). The graph is the straight line connecting them.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-26.png\" alt=\"\" class=\"wp-image-11615\" style=\"width:454px;height:auto\"\/><\/figure><\/div><\/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\/78260\/667\/895\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-129.png\" alt=\"\" class=\"wp-image-8088\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-129.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-129-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-129-150x150.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\/78263\/955\/107\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-138.png\" alt=\"\" class=\"wp-image-8089\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-138.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-138-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-138-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Standard form: graph an equation T.16 Standard form: graph an equation by Delta publications key notes: Standard Form Reminder A linear equation in standard form looks like this: Ax+By=C where A, B, and C are integers (no fractions), and x,y are variables. Why Use Intercepts to Graph? Step-by-Step Guide to Graph Using Intercepts Step What<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-16-standard-form-graph-an-equation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.16 Standard form: graph an equation&#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-329","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/329","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=329"}],"version-history":[{"count":18,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/329\/revisions"}],"predecessor-version":[{"id":17557,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/329\/revisions\/17557"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=329"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}