{"id":294,"date":"2022-04-13T08:58:38","date_gmt":"2022-04-13T08:58:38","guid":{"rendered":"http:\/\/9thclass.deltapublications.in\/?page_id=294"},"modified":"2024-10-23T16:10:05","modified_gmt":"2024-10-23T16:10:05","slug":"s-5-write-and-solve-direct-variation-equations","status":"publish","type":"page","link":"https:\/\/9thclass.deltapublications.in\/index.php\/s-5-write-and-solve-direct-variation-equations\/","title":{"rendered":"S.5 Write and solve direct variation equations"},"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>Write and solve direct variation equations<\/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>Direct Variation<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A direct variation is a relationship between two quantities where one quantity varies directly with the other.<\/li>\n\n\n\n<li>In other words, if one quantity increases, the other quantity also increases at a constant rate, and vice versa.<\/li>\n<\/ul>\n\n\n\n<p><strong>Equation of Direct Variation<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A direct variation equation can be written in the form y = kx, where:\n<ul class=\"wp-block-list\">\n<li>y is the dependent variable<\/li>\n\n\n\n<li>x is the independent variable<\/li>\n\n\n\n<li>k is the constant of variation<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n<p><strong>Finding the Constant of Variation<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To find the constant of variation, divide the dependent variable by the independent variable for any pair of corresponding values.<\/li>\n<\/ul>\n\n\n\n<p><strong>Solving Direct Variation Equations<\/strong><\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Substitute the known values:<\/strong> Substitute the known values for the variables into the direct variation equation.<\/li>\n\n\n\n<li><strong>Solve for the unknown variable:<\/strong> Use algebraic methods to solve for the unknown variable.<\/li>\n<\/ol>\n\n\n\n<p><strong>Example:<\/strong><\/p>\n\n\n\n<p>If y varies directly with x, and y = 12 when x = 4, find the equation of variation and the value of y when x = 7.<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Find the constant of variation:<\/strong> k = y\/x = 12\/4 = 3<\/li>\n\n\n\n<li><strong>Write the equation of variation:<\/strong> y = 3x<\/li>\n\n\n\n<li><strong>Find y when x = 7:<\/strong> y = 3(7) = 21<\/li>\n<\/ol>\n\n\n\n<p><strong>Key Points to Remember:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A direct variation is a relationship where one quantity varies directly with the other.<\/li>\n\n\n\n<li>The equation of direct variation is y = kx, where k is the constant of variation.<\/li>\n\n\n\n<li>To find the constant of variation, divide the dependent variable by the independent variable.<\/li>\n\n\n\n<li>To solve a direct variation equation, substitute the known values and solve for the unknown variable.<\/li>\n<\/ul>\n\n\n\n<p><\/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<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:#d6f0ce\"><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>Assume that <em>y<\/em> varies directly with x.If <em>y<\/em>&nbsp;= 18 when <em>x<\/em>&nbsp;= 3, find <em>y<\/em> when <em>x<\/em>&nbsp;=2.<\/strong><\/p>\n\n\n\n<p><em>Write and solve a direct variation equation to find the answer.<\/em><\/p>\n\n\n\n<p>y=______<\/p>\n<\/div><\/div>\n\n\n\n<p>First find the constant of variation. Plug <em>x<\/em>&nbsp;= 3 and <em>y<\/em>&nbsp;=18 into the direct variation equation and then solve for k.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em><br>18&nbsp;=&nbsp;<em>k<\/em>(3)<br>6&nbsp;=&nbsp;<em>k<\/em><\/p>\n\n\n\n<p>Now use <em>k<\/em>=6 to write the direct variation equation.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em><br><em>y<\/em>&nbsp;=&nbsp;6<em>x<\/em><\/p>\n\n\n\n<p>The direct variation equation is <em>y<\/em>&nbsp;= 6<em>x<\/em>.<\/p>\n\n\n\n<p>Finally, use the direct variation equation to find <em>y<\/em> when x=2.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;6<em>x<\/em><br><em>y<\/em>&nbsp;=&nbsp;6(2)<br><em>y<\/em>&nbsp;=&nbsp;12<\/p>\n\n\n\n<p>so,<\/p>\n\n\n\n<p>y =12.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#e9fcd0\"><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>If <em>y<\/em> varies directly with <em>x<\/em> and <em>y<\/em>&nbsp;= 20 when <em>x<\/em>&nbsp;= 4, find <em>y<\/em> when <em>x<\/em>&nbsp;=2.<\/strong><\/p>\n\n\n\n<p><em>Write and solve a direct variation equation to find the answer.<\/em><\/p>\n\n\n\n<p>y=________<\/p>\n<\/div><\/div>\n\n\n\n<p>First find the constant of variation. Plug <em>x<\/em>&nbsp;= 4 and <em>y<\/em>&nbsp;=20 into the direct variation equation and then solve for k.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em><br>20&nbsp;=&nbsp;<em>k<\/em>(4)<br>5&nbsp;=&nbsp;<em>k<\/em><\/p>\n\n\n\n<p>Now use <em>k<\/em>=5 to write the direct variation equation.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em><br><em>y<\/em>&nbsp;=&nbsp;5<em>x<\/em><\/p>\n\n\n\n<p>The direct variation equation is <em>y<\/em>&nbsp;= 5x.<\/p>\n\n\n\n<p>Finally, use the direct variation equation to find <em>y<\/em> when <em>x<\/em>&nbsp;=2.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;5<em>x<\/em><br><em>y<\/em>&nbsp;=&nbsp;5(2)<br><em>y<\/em>&nbsp;=&nbsp;10<\/p>\n\n\n\n<p>so,<\/p>\n\n\n\n<p>y =10.<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group has-background\" style=\"background-color:#d2ecff\"><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>If <em>y<\/em> varies directly with <em>x<\/em> and <em>y<\/em>&nbsp;= 20 when <em>x<\/em>&nbsp;= 10, find <em>y<\/em> when <em>x<\/em>=4.<\/strong><\/p>\n\n\n\n<p><em>Write and solve a direct variation equation to find the answer<\/em>.<\/p>\n\n\n\n<p>y=__________<\/p>\n<\/div><\/div>\n\n\n\n<p>First find the constant o fvariation. Plug <em>x<\/em>&nbsp;= 10 and <em>y<\/em>&nbsp;=20 into the direct variation equation and then solve for k.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em><br>20&nbsp;=&nbsp;<em>k<\/em>(10)<br>2&nbsp;=&nbsp;<em>k<\/em><\/p>\n\n\n\n<p>Now use <em>k<\/em>=2 to write the direct variation equation.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;<em>kx<\/em><br><em>y<\/em>&nbsp;=&nbsp;2<em>x<\/em><\/p>\n\n\n\n<p>The direct variation equation is <em>y<\/em>&nbsp;= 2<em>x<\/em>.<\/p>\n\n\n\n<p>Finally, use the direct variation equation to find <em>y<\/em> when <em>x<\/em>=4.<\/p>\n\n\n\n<p><em>y<\/em>&nbsp;=&nbsp;2<em>x<\/em><br><em>y<\/em>&nbsp;=&nbsp;2(4)<br><em>y<\/em>&nbsp;=&nbsp;8<\/p>\n\n\n\n<p>so <\/p>\n\n\n\n<p>y = 8.<\/p>\n<\/div><\/div>\n\n\n\n<p class=\"has-text-color\" 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\/80331\/230\/712\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-106.png\" alt=\"\" class=\"wp-image-8015\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-106.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-106-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-3-106-150x150.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\/80321\/833\/756\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"500\" src=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-115.png\" alt=\"\" class=\"wp-image-8016\" srcset=\"https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-115.png 500w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-115-300x300.png 300w, https:\/\/9thclass.deltapublications.in\/wp-content\/uploads\/2023\/05\/Worksheet-1-1-2-115-150x150.png 150w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/a><\/figure>\n<\/div>\n<\/div>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Write and solve direct variation equations Key Notes: Direct Variation Equation of Direct Variation Finding the Constant of Variation Solving Direct Variation Equations Example: If y varies directly with x, and y = 12 when x = 4, find the equation of variation and the value of y when x = 7. Key Points to<a class=\"more-link\" href=\"https:\/\/9thclass.deltapublications.in\/index.php\/s-5-write-and-solve-direct-variation-equations\/\">Continue reading <span class=\"screen-reader-text\">&#8220;S.5 Write and solve direct variation equations&#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-294","page","type-page","status-publish","hentry","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/294","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=294"}],"version-history":[{"count":19,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/294\/revisions"}],"predecessor-version":[{"id":15666,"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/pages\/294\/revisions\/15666"}],"wp:attachment":[{"href":"https:\/\/9thclass.deltapublications.in\/index.php\/wp-json\/wp\/v2\/media?parent=294"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}