{"id":300,"date":"2022-04-13T08:59:53","date_gmt":"2022-04-13T08:59:53","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=300"},"modified":"2025-08-20T01:26:11","modified_gmt":"2025-08-20T01:26:11","slug":"t-2-find-the-slope-of-a-graph","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-2-find-the-slope-of-a-graph\/","title":{"rendered":"T.2 Find the slope of a graph"},"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>Find the slope of a graph<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-link-color has-huge-font-size wp-elements-ac2bc047fac346cd34a46d2a76287634\" style=\"color:#74008b;text-transform:capitalize\">key notes:<\/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\" 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\/DAGwOPwMBPs\/C2QPw-0OSXY2FYCfUae-dw\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwOPwMBPs&#x2F;C2QPw-0OSXY2FYCfUae-dw&#x2F;watch?utm_content=DAGwOPwMBPs&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.2 Find the slope of a graph<\/a> by Delta publications\n<\/div>\n<\/div>\n\n\n\n<h3 class=\"wp-block-heading has-text-color has-link-color has-large-font-size wp-elements-f1577186fd9dc3728b7414e1673eb95b\" style=\"color:#000060\"><strong>What is Slope?<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The <strong>slope<\/strong> of a line tells how steep the line is.<\/li>\n\n\n\n<li>It measures the rate of change between two points on a line.<\/li>\n\n\n\n<li>In mathematics, slope is often denoted by the letter <strong>m<\/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-409e6bb5ebeef4ebfd763481d25ce312\" style=\"color:#000060\"><strong>Formula for Slope<\/strong><\/h3>\n\n\n\n<p>If you know two points on the line, (x1,y1) and (x2,y2)\u200b\u200b<\/p>\n\n\n\n<p>m = <strong>y2\u2212y1\u200b<\/strong> \/ <strong>x2\u2212x1<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>y2\u2212y1\u200b<\/strong> \u2192 change in y (rise)<\/li>\n\n\n\n<li><strong>x2\u2212x1\u200b<\/strong> \u2192 change in x (run)<\/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-41725451ce1bbb36a651e2b3491f46bc\" style=\"color:#000060\"><strong>Rise and Run<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Rise<\/strong> \u2192 how much the line goes up or down.<\/li>\n\n\n\n<li><strong>Run<\/strong> \u2192 how much the line goes left or right.<\/li>\n\n\n\n<li><strong>Slope = Rise \u00f7 Run<\/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-4e4750be677a63e2223f0b2fd4439b01\" style=\"color:#000060\"><strong>Types of Slopes<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive slope<\/strong> \u2192 line goes upward from left to right.<\/li>\n\n\n\n<li><strong>Negative slope<\/strong> \u2192 line goes downward from left to right.<\/li>\n\n\n\n<li><strong>Zero slope<\/strong> \u2192 horizontal line (no rise).<\/li>\n\n\n\n<li><strong>Undefined slope<\/strong> \u2192 vertical line (run = 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-5c130c2379c98cadbe74be3f259204e4\" style=\"color:#000060\"><strong>Steps to Find the Slope from a Graph<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Choose any two points exactly on the line.<\/li>\n\n\n\n<li>Label them (x1 , y1) and (x2 , y2) .<\/li>\n\n\n\n<li>Find the <strong>rise<\/strong> (y2 \u2212 y1 and <strong>run<\/strong> (x2 \u2212 x1\u200b).<\/li>\n\n\n\n<li>Apply the slope formula: <\/li>\n<\/ul>\n\n\n\n<p class=\"has-text-align-center\"><strong>m = rise \/ runm <\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Simplify the fraction if possible.<\/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-83855b6869da04c6278f1e70533049f2\" style=\"color:#000060\"><strong>Examples<\/strong><\/h3>\n\n\n\n<p><strong>Example 1:<\/strong> Points (2,3) and (5,9)<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>m = 9 &#8211; 3 \/ 5 &#8211; 2 = 6\/3 = 2<\/strong><\/p>\n\n\n\n<p>Slope = <strong>2<\/strong> (positive).<\/p>\n\n\n\n<p><strong>Example 2:<\/strong> Points (4,7) and (1,10) <\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>m = 10 &#8211; 7 \/ 1 &#8211; 4 = 3 \/ -3 = &#8211;<\/strong>1<\/p>\n\n\n\n<p>Slope = <strong>\u20131<\/strong> (negative).<\/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-4a6f949d3be920389d06fd9d30c34c0f\" style=\"color:#000060\"><strong>Real-life Meaning<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In real-world graphs, slope can represent speed, cost per item, rate of change in temperature, etc.<\/li>\n\n\n\n<li>Example: If the slope is <strong>3<\/strong>, it means \u201cfor every 1 unit increase in xxx, yyy increases by 3 units.\u201d<\/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-799e1e19c0649c545e75fdfdd3e4b9c4\" style=\"color:#000060\"><strong>Quick Tips<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Always subtract in the same order for yyy and xxx.<\/li>\n\n\n\n<li>Avoid switching points randomly\u2014it changes the sign.<\/li>\n\n\n\n<li>Vertical line \u2192 slope undefined (division by zero).<\/li>\n\n\n\n<li>Horizontal line \u2192 slope = 0.<\/li>\n<\/ul>\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-large-font-size\" style=\"background-color:#99f6f6\"><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-constrained wp-block-group-is-layout-constrained\">\n<p>Look at this graph:<\/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\/1-70.png\" alt=\"\" class=\"wp-image-11879\" style=\"width:360px;height:auto\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-557e1fe6af9c5adec975084a0c830e9c\" style=\"color:#b00012\">What is the slope?<\/p>\n\n\n\n<p>Simplify your answer and write it as a proper fraction, improper fraction, or integer.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-large-font-size\">Find any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-16.png\" alt=\"\" class=\"wp-image-15032\" style=\"width:356px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-16.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-16-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-16-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-16-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Two points on the line are&nbsp;(10, 20)&nbsp;and&nbsp;(30, 30).&nbsp;Put those points into the slope formula.<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\"><strong>slope&nbsp;=&nbsp;change in&nbsp;<em>y<\/em> \/ change in&nbsp;<em>x<\/em><\/strong><\/p>\n\n\n\n<p class=\"has-foreground-color has-text-color\">= 30-20 \/ 30-10  [ plugin (10, 30) and (30, 30)  ]<\/p>\n\n\n\n<p>= 10\/20       (subtract)<\/p>\n\n\n\n<p>= 1\/2           (simplify)<\/p>\n\n\n\n<p class=\"has-text-align-center has-foreground-color has-text-color has-large-font-size\"><strong>The slope is 1\/2.<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#a5e6a6\"><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>Look at this graph:<\/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\/1-72.png\" alt=\"\" class=\"wp-image-11887\" style=\"width:353px;height:auto\"\/><\/figure><\/div>\n\n\n<p class=\"has-text-color has-link-color wp-elements-557e1fe6af9c5adec975084a0c830e9c\" style=\"color:#b00012\">What is the slope?<\/p>\n\n\n\n<p>Simplify your answer and write it as a proper fraction, improper fraction, or integer.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-large-font-size\">Find any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-17.png\" alt=\"\" class=\"wp-image-15033\" style=\"width:360px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-17.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-17-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-17-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/08\/image-removebg-preview-17-400x400.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Two points on the line are&nbsp;(1, 5)&nbsp;and&nbsp;(3, 6).&nbsp;Put those points into the slope formula.<\/p>\n\n\n\n<p><strong>slope = change in y \/ change in x<\/strong><\/p>\n\n\n\n<p>= 6 &#8211; 5 \/ 3 &#8211; 1      Plugin (1,&nbsp;5) and (3,&nbsp;6)<\/p>\n\n\n\n<p>= 1\/2             Subtract<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>The slope is 1\/2.<\/strong><\/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\/77080\/132\/112\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-116.png\" alt=\"\" class=\"wp-image-8048\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-116.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-116-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-116-150x150.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\/76811\/575\/508\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-125.png\" alt=\"\" class=\"wp-image-8049\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-125.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-125-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-125-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Find the slope of a graph key notes: T.2 Find the slope of a graph by Delta publications What is Slope? Formula for Slope If you know two points on the line, (x1,y1) and (x2,y2)\u200b\u200b m = y2\u2212y1\u200b \/ x2\u2212x1 Rise and Run Types of Slopes Steps to Find the Slope from a Graph m<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-2-find-the-slope-of-a-graph\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.2 Find the slope of a graph&#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-300","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/300","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=300"}],"version-history":[{"count":25,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/300\/revisions"}],"predecessor-version":[{"id":17543,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/300\/revisions\/17543"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=300"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}