{"id":302,"date":"2022-04-13T09:00:08","date_gmt":"2022-04-13T09:00:08","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=302"},"modified":"2025-08-20T01:27:35","modified_gmt":"2025-08-20T01:27:35","slug":"t-3-find-the-slope-from-two-points","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/t-3-find-the-slope-from-two-points\/","title":{"rendered":"T.3 Find the slope from two points"},"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 from two points<\/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\/DAGwOLZtjIw\/v_XfACAEU_YU_O1olBKI4A\/watch?embed\" allowfullscreen=\"allowfullscreen\" allow=\"fullscreen\">\n  <\/iframe>\n<\/div>\n<a href=\"https:&#x2F;&#x2F;www.canva.com&#x2F;design&#x2F;DAGwOLZtjIw&#x2F;v_XfACAEU_YU_O1olBKI4A&#x2F;watch?utm_content=DAGwOLZtjIw&amp;utm_campaign=designshare&amp;utm_medium=embeds&amp;utm_source=link\" target=\"_blank\" rel=\"noopener\">T.3 Find the slope from two points<\/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-e1411710dcbc9b9c4cafe7aeefdcb74c\" style=\"color:#74008b;text-transform:capitalize\">key notes:<\/p>\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><strong>Slope<\/strong> tells us how steep a line is.<\/li>\n\n\n\n<li>It shows how much the <strong>y-value<\/strong> changes for every change in the <strong>x-value<\/strong>.<\/li>\n\n\n\n<li>Slope is also called the <strong>rate of change<\/strong> or <strong>gradient<\/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 two points on a line are <strong>(x\u2081, y\u2081)<\/strong> and <strong>(x\u2082, y\u2082)<\/strong>, the slope (<strong>m<\/strong>) is:<\/p>\n\n\n\n<p class=\"has-text-align-center\"><strong>\u200bm = y2 \u2212 y1 \/ x2 \u2212 x1<\/strong><\/p>\n\n\n\n<p><strong>Read as<\/strong>:<br>Slope = Change in y \u00f7 Change in x<br>or<br>Slope = <strong>rise<\/strong> \u00f7 <strong>run<\/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-0923fb42b9cde1ff486a21e663834348\" style=\"color:#000060\"><strong>Steps to Find the Slope<\/strong><\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Label the points<\/strong>: (x\u2081, y\u2081) and (x\u2082, y\u2082)<\/li>\n\n\n\n<li><strong>Subtract y-values<\/strong>: y2\u2212y1\u200b \u2192 this is the <strong>rise<\/strong>.<\/li>\n\n\n\n<li><strong>Subtract x-values<\/strong>: x2\u2212x1\u2192 this is the <strong>run<\/strong>.<\/li>\n\n\n\n<li><strong>Divide<\/strong>: rise \/ run<\/li>\n\n\n\n<li><strong>Simplify<\/strong> the fraction if possible.<\/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-8c705e1662000538b261543f7ab2b300\" style=\"color:#000060\"><strong>Example<\/strong><\/h3>\n\n\n\n<p>Find the slope of the line passing through (2, 5) and (6, 13): <\/p>\n\n\n\n<p>m = 13\u22125 \/ 6\u22122 = 8\/4 = 2<\/p>\n\n\n\n<p><strong>Slope = 2<\/strong> \u2192 For every 1 unit you move right, the line goes up by 2 units.<\/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-7e8595bd65142f9f45d4a3fb285383ca\" style=\"color:#000060\"><strong>Types of Slope<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Positive slope<\/strong>: Line goes <strong>up<\/strong> from left to right.<\/li>\n\n\n\n<li><strong>Negative slope<\/strong>: Line goes <strong>down<\/strong> from left to right.<\/li>\n\n\n\n<li><strong>Zero slope<\/strong>: Horizontal line (no rise).<\/li>\n\n\n\n<li><strong>Undefined slope<\/strong>: Vertical line (no 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-b740fa3e3c76de0010c808c9383a6d36\" style=\"color:#000060\"><strong>Common Mistakes<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Mixing up <strong>x<\/strong> and <strong>y<\/strong> values.<\/li>\n\n\n\n<li>Forgetting to subtract in the same order for both numerator and denominator.<\/li>\n\n\n\n<li>Dividing by zero (happens in vertical lines \u2192 slope is undefined).<\/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-4668900a84e12faeb2b7bcad7d70e5aa\" style=\"color:#000060\"><strong>Real-life Connection<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Slope is used in <strong>roads<\/strong>, <strong>ramps<\/strong>, <strong>roofs<\/strong>, and <strong>graphs<\/strong> to show steepness or rate of change.<\/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-large-font-size\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group has-background\" style=\"background-color:#f6eb98\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Find the slope of the line that passes through (9, 4) and (2, 2).<\/strong><\/p>\n\n\n\n<p>Plug (9, 4) and (2, 2) into the slope formula.<\/p>\n\n\n\n<p>Slope = change in&nbsp;<em>y<\/em> \/ change in&nbsp;<em>x<\/em><\/p>\n\n\n\n<p>           = 2-4 \/ 2-9 <\/p>\n\n\n\n<p>           = -2\/-7<\/p>\n\n\n\n<p>           = 2\/7<\/p>\n\n\n\n<p>The slope is 2\/7 .<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#99ffae\"><div class=\"wp-block-group__inner-container is-layout-flow wp-block-group-is-layout-flow\">\n<p class=\"has-background-background-color has-text-color has-background\" style=\"color:#b00012\"><strong>Find the slope of the line that passes through (4, 3) and (6, 4).<\/strong><\/p>\n\n\n\n<p>Plug (4, 3) and (6, 4) into the slope formula.<\/p>\n\n\n\n<p>Slope =change in&nbsp;<em>y<\/em> \/ change in&nbsp;<em>x<\/em><\/p>\n\n\n\n<p>           = 4-3 \/ 6-4<\/p>\n\n\n\n<p>           = 1\/2<\/p>\n\n\n\n<p class=\"has-text-align-center has-large-font-size\">The slope is 1\/2<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#b4aff8\"><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-text-color has-link-color wp-elements-51f0b1daf662f48047999243a28a2d2f\" style=\"color:#b00012\"><strong>Find the slope of the line that passes through (2, 5) and (8, 4).<\/strong><\/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>Plug (2, 5) and (8, 4) into the slope formula.<\/p>\n\n\n\n<p>slope = change in y \/ change in x<\/p>\n\n\n\n<p>= 4 &#8211; 5 \/ 8 &#8211; 2     <em>Plug in (<\/em><strong><em>2<\/em><\/strong><em>,&nbsp;<\/em><strong><em>5<\/em><\/strong><em>) and (<\/em><strong><em>8<\/em><\/strong><em>,&nbsp;<\/em><strong><em>4<\/em><\/strong><em>)<\/em><\/p>\n\n\n\n<p>= -1 \/ 6       Subtract<\/p>\n\n\n\n<p>The slope is -1 \/ 6 .<\/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<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\/611\/286\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-115.png\" alt=\"\" class=\"wp-image-8045\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-115.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-115-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-115-150x150.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\/76845\/898\/448\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-124.png\" alt=\"\" class=\"wp-image-8046\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-124.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-124-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-124-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Find the slope from two points T.3 Find the slope from two points by Delta publications key notes: What is Slope? Formula for Slope If two points on a line are (x\u2081, y\u2081) and (x\u2082, y\u2082), the slope (m) is: \u200bm = y2 \u2212 y1 \/ x2 \u2212 x1 Read as:Slope = Change in y<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/t-3-find-the-slope-from-two-points\/\">Continue reading <span class=\"screen-reader-text\">&#8220;T.3 Find the slope from two points&#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-302","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/302","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=302"}],"version-history":[{"count":22,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/302\/revisions"}],"predecessor-version":[{"id":17544,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/302\/revisions\/17544"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=302"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}