{"id":286,"date":"2022-04-13T08:57:28","date_gmt":"2022-04-13T08:57:28","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=286"},"modified":"2024-10-23T16:00:20","modified_gmt":"2024-10-23T16:00:20","slug":"s-1-identify-proportional-relationships","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/s-1-identify-proportional-relationships\/","title":{"rendered":"S.1 Identify proportional relationships"},"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>Identify proportional relationships<\/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>Key Characteristics of Proportional Relationships<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Constant Ratio:<\/strong> The ratio of the corresponding values of the two quantities is always the same.<\/li>\n\n\n\n<li><strong>Graph:<\/strong> When graphed, a proportional relationship forms a straight line passing through the origin (0, 0).<\/li>\n\n\n\n<li><strong>Equation:<\/strong> A proportional relationship can be represented by the equation y = kx, where k is the constant of proportionality.<\/li>\n<\/ul>\n\n\n\n<p><strong>Identifying Proportional Relationships<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Check the ratios:<\/strong> Calculate the ratios of corresponding values of the two quantities. If the ratios are constant, the relationship is proportional.<\/li>\n\n\n\n<li><strong>Graph the data:<\/strong> Plot the data points on a graph. If the points form a straight line passing through the origin, the relationship is proportional.<\/li>\n\n\n\n<li><strong>Check the equation:<\/strong> If the equation can be written in the form y = kx, where k is a constant, the relationship is proportional.<\/li>\n<\/ol>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>Consider the following table of values:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><th>x<\/th><th>y<\/th><\/tr><tr><td>2<\/td><td>6<\/td><\/tr><tr><td>4<\/td><td>12<\/td><\/tr><tr><td>6<\/td><td>18<\/td><\/tr><tr><td>8<\/td><td>24<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Export to Sheets<\/p>\n\n\n\n<p>To determine if the relationship is proportional, calculate the ratios of corresponding values:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>6\/2 = 3<\/li>\n\n\n\n<li>12\/4 = 3<\/li>\n\n\n\n<li>18\/6 = 3<\/li>\n\n\n\n<li>24\/8 = 3<\/li>\n<\/ul>\n\n\n\n<p>Since the ratios are constant, the relationship is proportional.<\/p>\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 has a constant ratio between the corresponding values of the two quantities.<\/li>\n\n\n\n<li>When graphed, a proportional relationship forms a straight line passing through the origin.<\/li>\n\n\n\n<li>A proportional relationship can be represented by the equation y = kx.<\/li>\n\n\n\n<li>To identify a proportional relationship, check the ratios, graph the data, or examine the equation.<\/li>\n<\/ul>\n\n\n\n<p class=\"has-large-font-size\"><\/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-large-font-size\" style=\"background-color:#cdeaf0\"><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>Look at this graph.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-81.png\" alt=\"\" class=\"wp-image-12202\" style=\"aspect-ratio:1;width:410px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-81.png 1000w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-81-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-81-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-81-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Is there a directly proportional relationship?<\/strong><\/p>\n\n\n\n<p><strong>yes       no<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You can tell that the relationship is not directly proportional by looking at the graph. The graph is a straight line, but it does not pass through the origin. So, the relationship is not directly proportional.<\/p>\n\n\n\n<p>You can also confirm that the linear relationship is not directly proportional by showing that the relationship cannot be written as&nbsp;<em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em>, where&nbsp;<em>k<\/em>&nbsp;is a constant ratio.<\/p>\n\n\n\n<p>First, create a chart. Use points from the graph, such as (2,&nbsp;6) and (4,&nbsp;9).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Jam made (litres)(y)<\/td><td>6<\/td><td>9<\/td><\/tr><tr><td>Days(x)<\/td><td>2<\/td><td>4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now divide &#8220;Jam made (litres)(y)&#8221; by &#8220;Days(x)&#8221; to find the ratio (k)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Jam made (litres)(y)<\/td><td>6<\/td><td>9<\/td><\/tr><tr><td>Days(x)<\/td><td>2<\/td><td>4<\/td><\/tr><tr><td>Ratio (k)<\/td><td>3<\/td><td>2.25<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The ratio (<em>k<\/em>) is not constant, so the relationship can&#8217;t be described by the equation&nbsp;<em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em>, where&nbsp;<em>k<\/em>&nbsp;is a constant ratio. This means that the relationship is not directly proportional.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#dcfcca\"><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>Look at this graph.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82.png\" alt=\"\" class=\"wp-image-12205\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82.png 1000w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Is the total number of pieces Lucy knows proportional to the number of weeks she takes lessons?<\/strong><\/p>\n\n\n\n<p><strong>yes       no<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You can tell that the relationship is directly proportional by looking at the graph. The graph is a straight line and it passes through the origin. So, the relationship is directly proportional.<\/p>\n\n\n\n<p>You can also confirm that the linear relationship is directly proportional by showing that the relationship can be written as&nbsp;<em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em>, where&nbsp;<em>k<\/em>&nbsp;is a constant ratio.<\/p>\n\n\n\n<p>First, create a chart. Use points from the graph, such as (1,&nbsp;1), (2,&nbsp;2), (3,&nbsp;3), and (4,&nbsp;4).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Number of Pieces learnt (y)<\/td><td>1<\/td><td>2<\/td><td>3<\/td><td>4<\/td><\/tr><tr><td>Number of weeks (x)<\/td><td>1<\/td><td>2<\/td><td>3<\/td><td>4<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now divide &#8220;Number of Pieces learnt (y)&#8221; by &#8220;Number of weeks (x)&#8221; to find the ratio (k) .<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Number of Pieces learnt (y)<\/td><td>1<\/td><td>2<\/td><td>3<\/td><td>4<\/td><\/tr><tr><td>Number of weeks (x)<\/td><td>1<\/td><td>2<\/td><td>3<\/td><td>4<\/td><\/tr><tr><td>Ratio (k)<\/td><td>1<\/td><td>1<\/td><td>1<\/td><td>1<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The ratio is constant (<em>k<\/em>&nbsp;= 1), so the relationship can be described by the equation&nbsp;<em>y<\/em>&nbsp;= 1<em>x<\/em>. This equation means that the number of pieces learnt is always 1 times the number of weeks.<\/p>\n\n\n\n<p>Because the relationship can be written as&nbsp;<em>y<\/em>&nbsp;= 1<em>x<\/em>, the relationship is directly proportional.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#c7effe\"><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>Look at this graph.<\/p>\n\n\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"1000\" height=\"1000\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-1.png\" alt=\"\" class=\"wp-image-12209\" style=\"aspect-ratio:1;width:416px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-1.png 1000w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-1-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-1-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-82-1-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>Is the total distance cycled proportional to the number of trips to work?<\/strong><\/p>\n\n\n\n<p><strong>yes       no<\/strong><\/p>\n<\/div><\/div>\n\n\n\n<p>You can tell that the relationship is not directly proportional by looking at the graph. The graph is a straight line, but it does not pass through the origin. So, the relationship is not directly proportional.<\/p>\n\n\n\n<p>You can also confirm that the linear relationship is not directly proportional by showing that the relationship cannot be written as&nbsp;<em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em>, where&nbsp;<em>k<\/em>&nbsp;is a constant ratio.<\/p>\n\n\n\n<p>First, create a chart. Use points from the graph, such as (1,&nbsp;3) and (6,&nbsp;10).<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Total distance cycled (kilimetres)(y)<\/td><td>3<\/td><td>10<\/td><\/tr><tr><td>Number of trips to work(x)<\/td><td>1<\/td><td>6<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>Now divide &#8220;Total distance cycled (kilimetres)(y)&#8221; by &#8220;Number of trips to work(x)&#8221; to find the ratio (k)<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><tbody><tr><td>Total distance cycled (kilimetres)(y)<\/td><td>3<\/td><td>10<\/td><\/tr><tr><td>Number of trips to work(x)<\/td><td>1<\/td><td>6<\/td><\/tr><tr><td>Ratio (k)<\/td><td>3<\/td><td>1.66<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p>The ratio (<em>k<\/em>) is not constant, so the relationship can&#8217;t be described by the equation&nbsp;<em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em>, where&nbsp;<em>k<\/em>&nbsp;is a constant ratio. This means that the relationship is not directly proportional.<\/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\/80324\/668\/220\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-109.png\" alt=\"\" class=\"wp-image-8024\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-109.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-109-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-109-150x150.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\/80308\/213\/326\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-118.png\" alt=\"\" class=\"wp-image-8026\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-118.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-118-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-118-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Identify proportional relationships Key Notes : Proportional Relationships Key Characteristics of Proportional Relationships Identifying Proportional Relationships Example: Consider the following table of values: x y 2 6 4 12 6 18 8 24 Export to Sheets To determine if the relationship is proportional, calculate the ratios of corresponding values: Since the ratios are constant, the<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/s-1-identify-proportional-relationships\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S.1 Identify proportional relationships&#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-286","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/286","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=286"}],"version-history":[{"count":20,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/286\/revisions"}],"predecessor-version":[{"id":15660,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/286\/revisions\/15660"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=286"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}