{"id":257543,"date":"2025-07-17T14:14:08","date_gmt":"2025-07-17T14:14:08","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=257543"},"modified":"2025-07-17T14:14:10","modified_gmt":"2025-07-17T14:14:10","slug":"the-value-of-y-varies-directly-with-x-2","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/17\/the-value-of-y-varies-directly-with-x-2\/","title":{"rendered":"The value of y varies directly with x"},"content":{"rendered":"\n
\"\"<\/figure>\n\n\n\n

The Correct Answer and Explanation is:<\/strong><\/p>\n\n\n\n

Correct Answer: 1 5\/7<\/strong><\/p>\n\n\n\n

\ud83d\udcd8 Explanation <\/h3>\n\n\n\n

This problem involves the concept of direct variation<\/strong>, which describes a relationship between two variables where one is a constant multiple of the other. Mathematically, this is expressed as:<\/p>\n\n\n\n

y=kxy = kx<\/p>\n\n\n\n

Here, yy varies directly with xx, meaning the ratio yx\\frac{y}{x} remains constant. This constant is denoted by kk, the constant of variation.<\/p>\n\n\n\n

We are given:<\/p>\n\n\n\n

    \n
  • y=247y = 2 \\frac{4}{7}<\/li>\n\n\n\n
  • x=37x = \\frac{3}{7}<\/li>\n<\/ul>\n\n\n\n

    First, convert the mixed number y=247y = 2 \\frac{4}{7} into an improper fraction:<\/p>\n\n\n\n

    247=1872 \\frac{4}{7} = \\frac{18}{7}<\/p>\n\n\n\n

    Now, calculate the constant of variation kk:<\/p>\n\n\n\n

    k=yx=187\u00f737=187\u00d773=12621=6k = \\frac{y}{x} = \\frac{18}{7} \\div \\frac{3}{7} = \\frac{18}{7} \\times \\frac{7}{3} = \\frac{126}{21} = 6<\/p>\n\n\n\n

    So, k=6k = 6. This means for any value of xx, the corresponding value of yy is 6x6x.<\/p>\n\n\n\n

    Now, we are asked to find the value of yy when x=27x = \\frac{2}{7}:<\/p>\n\n\n\n

    y=6\u00d727=127y = 6 \\times \\frac{2}{7} = \\frac{12}{7}<\/p>\n\n\n\n

    Convert 127\\frac{12}{7} into a mixed number:<\/p>\n\n\n\n

    127=157\\frac{12}{7} = 1 \\frac{5}{7}<\/p>\n\n\n\n

    Thus, the value of yy when x=27x = \\frac{2}{7} is 1 5\/7<\/strong>.<\/p>\n\n\n\n

    This solution demonstrates how direct variation allows us to maintain a consistent relationship between variables. By finding the constant of variation, we can easily compute new values without needing a graph or table.<\/p>\n\n\n\n

    \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

    The Correct Answer and Explanation is: Correct Answer: 1 5\/7 \ud83d\udcd8 Explanation This problem involves the concept of direct variation, which describes a relationship between two variables where one is a constant multiple of the other. Mathematically, this is expressed as: y=kxy = kx Here, yy varies directly with xx, meaning the ratio yx\\frac{y}{x} remains […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-257543","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257543","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=257543"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/257543\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=257543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=257543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=257543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}