{"id":323,"date":"2022-04-13T09:03:16","date_gmt":"2022-04-13T09:03:16","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=323"},"modified":"2025-08-20T01:40:20","modified_gmt":"2025-08-20T01:40:20","slug":"t-13-compare-linear-equations-graphs-and-tables","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-13-compare-linear-equations-graphs-and-tables\/","title":{"rendered":"T.13 Compare linear equations, graphs and tables"},"content":{"rendered":"\n<h2 class=\"wp-block-heading has-text-align-center has-text-color has-huge-font-size\" style=\"color:#0e0354;text-transform:uppercase\"><strong>Compare linear equations, graphs, and tables<\/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\/DAGwHnANP3I\/ez_8Ac7vE5Fy5bHBEPJMQQ\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwHnANP3I&#x2F;ez_8Ac7vE5Fy5bHBEPJMQQ&#x2F;watch?utm_content=DAGwHnANP3I&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.13 Compare linear equations, graphs and tables<\/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-4dde4300b7763c9a2a860fe18546dfe2\" style=\"color:#74008b;text-transform:uppercase\">key notes:<\/p>\n\n\n\n<p class=\"has-text-color has-link-color has-large-font-size wp-elements-b86b3f114ba0290d6802523a9d635d72\" style=\"color:#000060\"> <strong>What is a Linear Relationship?<\/strong><\/p>\n\n\n\n<p>A <strong>linear relationship<\/strong> shows a constant rate of change between two variables.<br>It can be represented in <strong>three main ways<\/strong>:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Equation<\/strong> \u2013 Algebraic form (e.g., y=2x+3)<\/li>\n\n\n\n<li><strong>Graph<\/strong> \u2013 A straight line on a coordinate plane<\/li>\n\n\n\n<li><strong>Table<\/strong> \u2013 A set of ordered pairs (x,y) showing the relationship<\/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 wp-elements-84debf5cf02dc897ef645046c229bc8f\" style=\"color:#000060\"><strong> Forms of a Linear Equation<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Slope-Intercept Form<\/strong>:<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>y=mx+b<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>mmm = slope (rate of change)<\/li>\n\n\n\n<li>bbb = y-intercept (where the line crosses the y-axis)<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-left\"><strong>Standard Form<\/strong>:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>Ax+By=C<\/strong><\/p>\n\n\n\n<p>Can be converted to slope-intercept form to compare easily<\/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-dbc2a222d066606c4b1b1cd71433c918\" style=\"color:#000060\"><strong> How to Compare Using Equations, Graphs, and Tables<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>A. Compare Slope (m)<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>In equation:<\/strong> Look directly at mmm in<\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>y=mx+b<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>In graph:<\/strong> Choose two points, use formula:<\/li>\n<\/ul>\n\n\n\n<p>m=change&nbsp;in&nbsp;y\/change&nbsp;in&nbsp;x &#8211; y<sub>2<\/sub>-y<sub>1<\/sub>\/ x<sub>2-<\/sub>x<sub>1<\/sub><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>In table:<\/strong> Check how much y changes when x increases by 1.<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>B. Compare Y-Intercept (b)<\/strong><\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>In equation:<\/strong> Look directly at bbb.<\/li>\n\n\n\n<li><strong>In graph:<\/strong> Find where the line crosses y-axis (x = 0).<\/li>\n\n\n\n<li><strong>In table:<\/strong> Look for the value of y when x = 0.<\/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-96c8fe54ec0a0f7c675330bf94b579c8\" style=\"color:#000060\"><strong>Worked Examples<\/strong><\/h3>\n\n\n\n<h4 class=\"wp-block-heading has-large-font-size\"><strong>Example 1 \u2013 Compare from Equations<\/strong><\/h4>\n\n\n\n<p>Equation 1: y=2x+5<br>Equation 2: y=2x\u22123<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slopes: both m=2\u2192 lines are <strong>parallel<\/strong> (same steepness).<\/li>\n\n\n\n<li>Intercepts: 5 vs -3 \u2192 different starting points on y-axis.<\/li>\n<\/ul>\n\n\n\n<p>\u2705 Lines have same slope, different intercepts \u2192 parallel lines.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Example 2 \u2013 Compare from Graphs<\/strong><\/h4>\n\n\n\n<p>If one line rises faster than another when moving left to right, it has a <strong>larger slope<\/strong>.<br>If lines cross y-axis at different points, they have different <strong>y-intercepts<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h4 class=\"wp-block-heading\"><strong>Example 3 \u2013 Compare from Tables<\/strong><\/h4>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><thead><tr><th>x<\/th><th>y\u2081<\/th><th>y\u2082<\/th><\/tr><\/thead><tbody><tr><td>0<\/td><td>4<\/td><td>1<\/td><\/tr><tr><td>1<\/td><td>6<\/td><td>3<\/td><\/tr><tr><td>2<\/td><td>8<\/td><td>5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slope for y<sub>1<\/sub>\u200b: increase by 2 each time x increases by 1 \u2192 slope = 2.<\/li>\n\n\n\n<li>Slope for y<sub>2<\/sub>\u200b: also increase by 2 \u2192 slope = 2.<\/li>\n\n\n\n<li>Intercept for y<sub>1<\/sub> = 4, for y<sub>2<\/sub>= 1.<\/li>\n<\/ul>\n\n\n\n<p>\u2705 Same slope, different intercepts \u2192 parallel.<\/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-5da734ff5923688eb54e276e9f9acb3c\" style=\"color:#000060\"><strong>Common Observations When Comparing<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Same slope, different intercept<\/strong> \u2192 parallel lines.<\/li>\n\n\n\n<li><strong>Different slope<\/strong> \u2192 lines intersect at one point.<\/li>\n\n\n\n<li><strong>Same slope and intercept<\/strong> \u2192 same line (overlapping). <\/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-a08ab681eb7d7f232ba2b0a20e92f38c\" style=\"color:#000060\"><strong>Practice Questions<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Compare y=3x+1 and y=3x\u22124<\/li>\n\n\n\n<li>Compare the lines with points (0, 2) &amp; (2, 6) and (0, 1) &amp; (2, 7).<\/li>\n\n\n\n<li>From the table:<\/li>\n<\/ul>\n\n\n\n<p>| x | y\u2081 | y\u2082 |<br>| &#8211; | &#8212; | &#8212; |<br>| 0 | 5 | 7 |<br>| 1 | 8 | 9 |<br>| 2 | 11 | 11 |<br>Compare slopes and intercepts.<\/p>\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:#e6cdfc\"><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>Function&nbsp;A and Function B are linear&nbsp;functions.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-19.png\" alt=\"\" class=\"wp-image-11592\" style=\"width:387px;height:auto\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-45b985f50265a6608852865c7d4f244b\" style=\"color:#b00012\">Which&nbsp;statement is&nbsp;true?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The&nbsp;slope of Function A is greater than the slope of Function&nbsp;B.<\/li>\n\n\n\n<li>The&nbsp;slope of Function A is less than the slope of Function&nbsp;B.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p>Find the slope of Function A.<\/p>\n\n\n\n<p>The graph of a linear function is a line. Find the change in y and the change in x between any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-20.png\" alt=\"\" class=\"wp-image-11593\" style=\"aspect-ratio:0.9966996699669967;width:426px;height:auto\"\/><\/figure><\/div>\n\n\n<p>The&nbsp;change in&nbsp;<em>y<\/em>&nbsp;is&nbsp;2,&nbsp;and the change in&nbsp;<em>x<\/em>&nbsp;is&nbsp;2.<\/p>\n\n\n\n<p>The&nbsp;slope&nbsp;is:<\/p>\n\n\n\n<p>m = change&nbsp;in&nbsp;<em>y<\/em> \/ change&nbsp;in&nbsp;x<\/p>\n\n\n\n<p>m = 2\/2<\/p>\n\n\n\n<p>m = 1<\/p>\n\n\n\n<p>Find the slope of Function B.<\/p>\n\n\n\n<p>The equation is in slope-intercept form, y=2x+4.<\/p>\n\n\n\n<p>So, the slope is 2.<\/p>\n\n\n\n<p>Compare the slopes.<\/p>\n\n\n\n<p>The slope of Function A is 1. The slope of Function B is 2.<\/p>\n\n\n\n<p>So, the slope of Function A is<strong> less than<\/strong> the slope of Function B.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-normal-font-size\" style=\"background-color:#fad2e7\"><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 has-normal-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>Function&nbsp;A and Function B are linear&nbsp;functions.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-21.png\" alt=\"\" class=\"wp-image-11595\" style=\"width:465px;height:auto\"\/><\/figure>\n\n\n\n<p class=\"has-text-color has-link-color wp-elements-45b985f50265a6608852865c7d4f244b\" style=\"color:#b00012\">Which&nbsp;statement is&nbsp;true?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The&nbsp;slope of Function A is greater than the slope of Function&nbsp;B.<\/li>\n\n\n\n<li>The&nbsp;slope of Function A is less than the slope of Function&nbsp;B.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<p><strong>Find the slope of Function A.<\/strong><\/p>\n\n\n\n<p>The equation is in slope-intercept form, y=x\u20135.<\/p>\n\n\n\n<p>Since y=x\u20135 is the same as y=1x\u20135, the slope is 1.<\/p>\n\n\n\n<p><strong>Find the slope of Function B.<\/strong><\/p>\n\n\n\n<p>The graph of a linear function is a line. Find the change in y and the change in x between any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" src=\"https:\/\/10thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-22-1.png\" alt=\"\" class=\"wp-image-11597\" style=\"aspect-ratio:0.996875;width:433px;height:auto\"\/><\/figure><\/div>\n\n\n<p>The&nbsp;change in&nbsp;<em>y<\/em>&nbsp;is&nbsp;4,&nbsp;and the change in&nbsp;<em>x<\/em>&nbsp;is&nbsp;1.<\/p>\n\n\n\n<p>The&nbsp;slope&nbsp;is:<\/p>\n\n\n\n<p>m = change&nbsp;in&nbsp;<em>y<\/em> \/ change&nbsp;in&nbsp;x<\/p>\n\n\n\n<p>m = 4\/1<\/p>\n\n\n\n<p>m = 4<\/p>\n\n\n\n<p><strong>Compare<\/strong><strong>&nbsp;the&nbsp;<\/strong><strong>slopes.<\/strong><\/p>\n\n\n\n<p>The&nbsp;slope of Function A is&nbsp;1.&nbsp;The slope of Function B is&nbsp;4.<\/p>\n\n\n\n<p>So,&nbsp;the slope of Function A is&nbsp;<strong>less&nbsp;than<\/strong>&nbsp;the slope of Function&nbsp;B.<\/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\/78190\/374\/563\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-119.png\" alt=\"\" class=\"wp-image-8057\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-119.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-119-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-119-150x150.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\/78259\/426\/802\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128.png\" alt=\"\" class=\"wp-image-8058\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-128-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Compare linear equations, graphs, and tables T.13 Compare linear equations, graphs and tables by Delta publications key notes: What is a Linear Relationship? A linear relationship shows a constant rate of change between two variables.It can be represented in three main ways: Forms of a Linear Equation y=mx+b Standard Form: Ax+By=C Can be converted to<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-13-compare-linear-equations-graphs-and-tables\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.13 Compare linear equations, graphs and tables&#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-323","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/323","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=323"}],"version-history":[{"count":20,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/323\/revisions"}],"predecessor-version":[{"id":17553,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/323\/revisions\/17553"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=323"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}