{"id":288,"date":"2022-04-13T08:57:45","date_gmt":"2022-04-13T08:57:45","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=288"},"modified":"2024-10-23T16:03:16","modified_gmt":"2024-10-23T16:03:16","slug":"s-2-find-the-constant-of-variation","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/s-2-find-the-constant-of-variation\/","title":{"rendered":"S.2 Find the constant of variation"},"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>Find the constant of variation<\/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>Constant of Variation<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In a proportional relationship, the constant of variation is the constant ratio between the two quantities.<\/li>\n\n\n\n<li>It represents the rate at which one quantity changes with respect to the other.<\/li>\n<\/ul>\n\n\n\n<p><strong>Finding the Constant of Variation<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Identify the proportional relationship:<\/strong> Determine if the relationship between the two quantities is proportional.<\/li>\n\n\n\n<li><strong>Find a pair of corresponding values:<\/strong> Choose any pair of corresponding values for the two quantities.<\/li>\n\n\n\n<li><strong>Calculate the ratio:<\/strong> Divide the value of the second quantity by the value of the first quantity.<\/li>\n\n\n\n<li><strong>The result is the constant of variation.<\/strong><\/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 find the constant of variation, calculate the ratio of y to x for any pair of 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>Therefore, the constant of variation is 3.<\/p>\n\n\n\n<p><strong>Key Points to Remember:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The constant of variation is the constant ratio between two quantities in a proportional relationshi<\/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:#dfe5f5\"><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>This graph shows how the total number of pieces Lola has learnt depends on the number of weeks she has taken piano lessons.<\/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\/1-84.png\" alt=\"\" class=\"wp-image-12213\" style=\"aspect-ratio:1;width:438px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-84.png 1000w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-84-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-84-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-84-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What is the constant of variation?<\/strong><\/p>\n\n\n\n<p>Write your answer as a decimal or integer.<\/p>\n\n\n\n<p>&nbsp;_______pieces per week.<\/p>\n<\/div><\/div>\n\n\n\n<p>Find any two points on the line.<\/p>\n\n\n<div class=\"wp-block-image is-resized\">\n<figure class=\"aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__85_-removebg-preview.png\" alt=\"\" class=\"wp-image-12215\" style=\"aspect-ratio:1;width:442px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__85_-removebg-preview.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__85_-removebg-preview-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1__85_-removebg-preview-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p>Two points on the line are&nbsp;(0, 0)&nbsp;and&nbsp;(2, 3).&nbsp;Put those points into the slope formula.<\/p>\n\n\n\n<p>slope&nbsp;=&nbsp;change in&nbsp;<em>y<\/em>\/change in&nbsp;<em>x<\/em><\/p>\n\n\n\n<p><br>&nbsp;=&nbsp;3-0\/2-0       <em>Plug in (<strong>0<\/strong>,&nbsp;<strong>0<\/strong>) and (<strong>2<\/strong>,&nbsp;<strong>3<\/strong>)<\/em><br>&nbsp;=&nbsp;3\/2            <em>Subtract<\/em><br>&nbsp;=&nbsp;1.5        <em>Write as a decimal<\/em><br>The slope is 1.5. The constant of variation is 1.50 pieces per week.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#e8def8\"><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>This graph shows how the total number of souvenirs Vijay buys is related to the number of days he spends on holiday.<\/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\/01\/image-removebg-preview-2024-01-06T155619.267.png\" alt=\"\" class=\"wp-image-12225\" style=\"aspect-ratio:1;width:398px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-06T155619.267.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-06T155619.267-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/image-removebg-preview-2024-01-06T155619.267-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What is the constant of variation?<\/strong><\/p>\n\n\n\n<p>Write your answer as a decimal or integer.<\/p>\n\n\n\n<p>_______souvenirs per day.<\/p>\n<\/div><\/div>\n\n\n\n<p>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=\"1000\" height=\"1000\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-88.png\" alt=\"\" class=\"wp-image-12224\" style=\"aspect-ratio:1;width:378px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-88.png 1000w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-88-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-88-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-88-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>Two points on the line are&nbsp;(0, 0)&nbsp;and&nbsp;(40, 30).&nbsp;Put those points into the slope formula.<\/p>\n\n\n\n<p>slope&nbsp;=&nbsp;change in x\/change in y<\/p>\n\n\n\n<p>=30-0\/40-0         <em>Plug in (<\/em><strong><em>0<\/em><\/strong><em>,&nbsp;<\/em><strong><em>0<\/em><\/strong><em>) and (<\/em><strong><em>40<\/em><\/strong><em>,&nbsp;<\/em><strong><em>30<\/em><\/strong><em>)<\/em><br>&nbsp;=&nbsp;30\/40  <em>Subtract<\/em><\/p>\n\n\n\n<p>=3\/4       <em>Simplify<\/em><br>&nbsp;=&nbsp;0.75      <em>Write as a decimal<\/em><br>The slope is 0.75. The constant of variation is 0.75 souvenirs per day.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background has-large-font-size\" style=\"background-color:#cdf9d0\"><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>This graph shows how the length of Frank&#8217;s essay depends on the number of hours he spends writing this week.<\/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\/1-89.png\" alt=\"\" class=\"wp-image-12242\" style=\"aspect-ratio:1;width:356px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-89.png 1000w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-89-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-89-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-89-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p class=\"has-text-color\" style=\"color:#b00012\"><strong>What is the constant of variation?<\/strong><\/p>\n\n\n\n<p>Write your answer as a decimal or integer.<\/p>\n\n\n\n<p>______pages per hour.<\/p>\n<\/div><\/div>\n\n\n\n<p>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=\"1000\" height=\"1000\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-90.png\" alt=\"\" class=\"wp-image-12248\" style=\"aspect-ratio:1;width:358px;height:auto\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-90.png 1000w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-90-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-90-150x150.png 150w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2024\/01\/1-90-768x768.png 768w\" sizes=\"auto, (max-width: 1000px) 100vw, 1000px\" \/><\/figure><\/div>\n\n\n<p>Two points on the line are&nbsp;(0, 0)&nbsp;and&nbsp;(40, 10).&nbsp;Put those points into the slope formula.<\/p>\n\n\n\n<p>slope&nbsp;=&nbsp;change in&nbsp;<em>y<\/em>\/change in&nbsp;<em>x<\/em><\/p>\n\n\n\n<p><br>&nbsp;=&nbsp;10-0\/40-0       <em>Plug in (<strong>0<\/strong>,&nbsp;<strong>0<\/strong>) and (<strong>40<\/strong>,&nbsp;<strong>10<\/strong>)<\/em><br>&nbsp;=&nbsp;10\/40            Subtract<br>&nbsp;=&nbsp;1\/4             Simplify<br>&nbsp;=&nbsp;0.25         Write as a decimal<br>The slope is 0.25. The constant of variation is 0.25 pages per hour.<\/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\/80326\/839\/596\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110.png\" alt=\"\" class=\"wp-image-8028\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-110-150x150.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\/423\/944\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-119.png\" alt=\"\" class=\"wp-image-8029\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-119.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-119-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-119-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Find the constant of variation Key Notes : Constant of Variation Finding the Constant of Variation Example: Consider the following table of values: x y 2 6 4 12 6 18 8 24 Export to Sheets To find the constant of variation, calculate the ratio of y to x for any pair of values: Therefore,<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/s-2-find-the-constant-of-variation\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S.2 Find the constant of variation&#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-288","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/288","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=288"}],"version-history":[{"count":20,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/288\/revisions"}],"predecessor-version":[{"id":15662,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/288\/revisions\/15662"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=288"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}