{"id":290,"date":"2022-04-13T08:58:05","date_gmt":"2022-04-13T08:58:05","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=290"},"modified":"2024-10-23T16:06:16","modified_gmt":"2024-10-23T16:06:16","slug":"s-3-graph-a-proportional-relationship","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/s-3-graph-a-proportional-relationship\/","title":{"rendered":"S.3 Graph a proportional relationship"},"content":{"rendered":"\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<h2 class=\"wp-block-heading has-text-align-center has-text-color\" style=\"color:#00056d;text-transform:uppercase\"><strong>Graph a proportional relationship<\/strong><\/h2>\n\n\n\n<p class=\"has-text-color has-huge-font-size\" style=\"color:#74008b\">Key Notes:<\/p>\n\n\n\n<p><strong>Proportional Relationships<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A proportional relationship is a relationship between two quantities that can be expressed as a constant ratio or rate.<\/li>\n\n\n\n<li>In other words, if two quantities are proportional, their ratio remains constant.<\/li>\n<\/ul>\n\n\n\n<p><strong>Graphing Proportional Relationships<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>When graphed, a proportional relationship forms a straight line passing through the origin (0, 0).<\/li>\n\n\n\n<li>The slope of the line represents the constant of proportionality.<\/li>\n<\/ul>\n\n\n\n<p><strong>Steps to Graph a Proportional Relationship:<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the constant of proportionality:<\/strong> Find the constant ratio between the two quantities.<\/li>\n\n\n\n<li><strong>Plot the origin:<\/strong> Plot the point (0, 0) on the coordinate plane.<\/li>\n\n\n\n<li><strong>Use the constant of proportionality to find additional points:<\/strong> Choose a value for one of the quantities and multiply it by the constant of proportionality to find the corresponding value of the other quantity. Plot the point representing this pair of values.<\/li>\n\n\n\n<li><strong>Draw a line:<\/strong> Draw a straight line passing through the origin and the point you plotted.<\/li>\n<\/ol>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>Consider the proportional relationship y = 2x.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The constant of proportionality is 2.<\/li>\n\n\n\n<li>Plot the point (0, 0).<\/li>\n\n\n\n<li>Choose a value for x, such as x = 3. Multiply it by the constant of proportionality: y = 2 * 3 = 6. Plot the point (3, 6).<\/li>\n\n\n\n<li>Draw a straight line passing through (0, 0) and (3, 6).<\/li>\n<\/ul>\n\n\n\n<p><strong>Key Points to Remember:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A proportional relationship forms a straight line passing through the origin when graphed.<\/li>\n\n\n\n<li>The slope of the line represents the constant of proportionality.<\/li>\n\n\n\n<li>To graph a proportional relationship, plot the origin and use the constant of proportionality to find additional points.<\/li>\n<\/ul>\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<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\" style=\"background-color:#caf2f5\"><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-text-color\" style=\"color:#b00012\"><strong>Graph&nbsp;this&nbsp;function:<\/strong><\/p>\n\n\n\n<p>y=2x<\/p>\n\n\n\n<p>Click&nbsp;to select points on the&nbsp;graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-17.png\" alt=\"\" class=\"wp-image-4973\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-17.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-17-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-17-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;ordered pairs by plugging in values for&nbsp;x.<\/p>\n\n\n\n<p><strong>Plug&nbsp;in&nbsp;<\/strong>x<strong>=<\/strong>\u2013<strong>5<\/strong>.<\/p>\n\n\n\n<p>y=2x<\/p>\n\n\n\n<p>=2(\u20135)<\/p>\n\n\n\n<p>=\u201310<\/p>\n\n\n\n<p>The&nbsp;point&nbsp;(\u20135,\u201310)&nbsp;is on the&nbsp;graph.<\/p>\n\n\n\n<p><strong>Plug&nbsp;in&nbsp;<\/strong>x<strong>=<\/strong>\u2013<strong>2<\/strong>.<\/p>\n\n\n\n<p>=2x<\/p>\n\n\n\n<p>=2(\u20132)<\/p>\n\n\n\n<p>=\u20134<\/p>\n\n\n\n<p>The&nbsp;point&nbsp;(\u20132,\u20134)&nbsp;is on the&nbsp;graph.<\/p>\n\n\n\n<p>Plot&nbsp;the points&nbsp;(\u20135,\u201310)&nbsp;and&nbsp;(\u20132,\u20134)&nbsp;on the&nbsp;graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-18.png\" alt=\"\" class=\"wp-image-4974\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-18.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-18-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__1_-removebg-preview-18-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;graph of the function&nbsp;y=2x&nbsp;is the straight line connecting the points&nbsp;(\u20135,\u201310)&nbsp;and&nbsp;(\u20132,\u20134).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-12.png\" alt=\"\" class=\"wp-image-4975\" style=\"width:457px;height:457px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-12.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-12-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__2_-removebg-preview-12-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#def0c2\"><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-text-color\" style=\"color:#b00012\"><strong>Graph&nbsp;this&nbsp;function:<\/strong><\/p>\n\n\n\n<p>y=\u20132x<\/p>\n\n\n\n<p>Click&nbsp;to select points on the&nbsp;graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2.png\" alt=\"\" class=\"wp-image-4979\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-2-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;ordered pairs by plugging in values for&nbsp;x.<\/p>\n\n\n\n<p><strong>Plug&nbsp;in&nbsp;<\/strong>x<strong>=<\/strong>\u2013<strong>3<\/strong>.<\/p>\n\n\n\n<p>y=\u20132x<\/p>\n\n\n\n<p>=\u20132(\u20133)<\/p>\n\n\n\n<p>=6<\/p>\n\n\n\n<p>he&nbsp;point&nbsp;(\u20133,6)&nbsp;is on the&nbsp;graph.<\/p>\n\n\n\n<p><strong>Plug&nbsp;in&nbsp;<\/strong>x<strong>=<\/strong>\u2013<strong>1<\/strong>.<\/p>\n\n\n\n<p>y=\u20132x<\/p>\n\n\n\n<p>=\u20132(\u20131)<\/p>\n\n\n\n<p>=2<\/p>\n\n\n\n<p>The&nbsp;point&nbsp;(\u20131,2)&nbsp;is on the&nbsp;graph.<\/p>\n\n\n\n<p>Plot&nbsp;the points&nbsp;(\u20133,6)&nbsp;and&nbsp;(\u20131,2)&nbsp;on the&nbsp;graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-10.png\" alt=\"\" class=\"wp-image-4980\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-10.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-10-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__4_-removebg-preview-10-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;graph of the function&nbsp;y=\u20132x&nbsp;is the straight line connecting the points&nbsp;(\u20133,6)&nbsp;and&nbsp;(\u20131,2).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9.png\" alt=\"\" class=\"wp-image-4981\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__5_-removebg-preview-9-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#d4f5e3\"><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-text-color\" style=\"color:#b00012\"><strong>Graph&nbsp;this&nbsp;function:<\/strong><\/p>\n\n\n\n<p>y=\u20132x<\/p>\n\n\n\n<p>Click&nbsp;to select points on the&nbsp;graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-3.png\" alt=\"\" class=\"wp-image-4984\" style=\"width:500px;height:500px\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled-design-3-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><figcaption class=\"wp-element-caption\"><br><br><\/figcaption><\/figure>\n<\/div><\/div>\n\n\n\n<p>Find&nbsp;ordered pairs by plugging in values for&nbsp;x<\/p>\n\n\n\n<p><strong>Plug&nbsp;in&nbsp;<\/strong>x<strong>=<\/strong>\u2013<strong>1<\/strong>.<\/p>\n\n\n\n<p>y=\u20132x<\/p>\n\n\n\n<p>=\u20132(\u20131)<\/p>\n\n\n\n<p>=2<\/p>\n\n\n\n<p>The&nbsp;point&nbsp;(\u20131,2)&nbsp;is on the&nbsp;graph.<\/p>\n\n\n\n<p><strong>Plug&nbsp;in&nbsp;<\/strong>x<strong>=2<\/strong>.<\/p>\n\n\n\n<p>y=\u20132x<\/p>\n\n\n\n<p>=\u20132(2)<\/p>\n\n\n\n<p>=\u20134<\/p>\n\n\n\n<p>The&nbsp;point&nbsp;(2,\u20134)&nbsp;is on the&nbsp;graph.<\/p>\n\n\n\n<p>Plot&nbsp;the points&nbsp;(\u20131,2)&nbsp;and&nbsp;(2,\u20134)&nbsp;on the&nbsp;graph.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview-6.png\" alt=\"\" class=\"wp-image-4985\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview-6.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview-6-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__7_-removebg-preview-6-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<p>The&nbsp;graph of the function&nbsp;y=\u20132x&nbsp;is the straight line connecting the points&nbsp;(\u20131,2)&nbsp;and&nbsp;(2,\u20134).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__8_-removebg-preview-3.png\" alt=\"\" class=\"wp-image-4986\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__8_-removebg-preview-3.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__8_-removebg-preview-3-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/02\/Untitled_design__8_-removebg-preview-3-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\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\/80328\/681\/688\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-108.png\" alt=\"\" class=\"wp-image-8021\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-108.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-108-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-108-150x150.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\/80310\/580\/145\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-117.png\" alt=\"\" class=\"wp-image-8022\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-117.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-117-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-117-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Graph a proportional relationship Key Notes: Proportional Relationships Graphing Proportional Relationships Steps to Graph a Proportional Relationship: Example: Consider the proportional relationship y = 2x. Key Points to Remember: Learn with an example Graph&nbsp;this&nbsp;function: y=2x Click&nbsp;to select points on the&nbsp;graph. Find&nbsp;ordered pairs by plugging in values for&nbsp;x. Plug&nbsp;in&nbsp;x=\u20135. y=2x =2(\u20135) =\u201310 The&nbsp;point&nbsp;(\u20135,\u201310)&nbsp;is on the&nbsp;graph. Plug&nbsp;in&nbsp;x=\u20132.<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/s-3-graph-a-proportional-relationship\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S.3 Graph a proportional relationship&#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-290","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/290","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=290"}],"version-history":[{"count":17,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/290\/revisions"}],"predecessor-version":[{"id":15664,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/290\/revisions\/15664"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=290"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}