{"id":228567,"date":"2025-06-07T11:52:51","date_gmt":"2025-06-07T11:52:51","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=228567"},"modified":"2025-06-07T11:52:52","modified_gmt":"2025-06-07T11:52:52","slug":"which-graph-represents-a-function-with-direct-variation","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/07\/which-graph-represents-a-function-with-direct-variation\/","title":{"rendered":"‘Which graph represents a function with direct variation"},"content":{"rendered":"\n

‘Which graph represents a function with direct variation<\/p>\n\n\n\n

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

\u2705 Correct Answer:<\/strong><\/h3>\n\n\n\n

A graph that is a straight line passing through the origin (0, 0)<\/strong> represents a function with direct variation.<\/p>\n\n\n\n

\n\n\n\n

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

A direct variation<\/strong> is a type of linear relationship between two variables where one variable is a constant multiple of the other. It can be expressed by the equation:y=kxy = kxy=kx<\/p>\n\n\n\n

Here, kkk<\/strong> is the constant of variation<\/strong> or slope<\/strong>, and it represents how much yyy changes for each unit change in xxx. This equation has no y-intercept<\/strong> other than 0, meaning the graph must pass through the origin (0, 0)<\/strong>.<\/p>\n\n\n\n

This is different from general linear equations like:y=mx+by = mx + by=mx+b<\/p>\n\n\n\n

where b\u22600b \\neq 0b\ue020=0 would cause the line not<\/strong> to pass through the origin. Such lines do not<\/strong> represent direct variation.<\/p>\n\n\n\n

Key Features of a Direct Variation Graph:<\/h3>\n\n\n\n
    \n
  1. Straight Line<\/strong> \u2013 The graph must be linear (not curved or broken).<\/li>\n\n\n\n
  2. Passes Through Origin<\/strong> \u2013 The point (0, 0) must be on the line.<\/li>\n\n\n\n
  3. Slope is Constant<\/strong> \u2013 The ratio yx\\frac{y}{x}xy\u200b is the same for all points.<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    \u26a0\ufe0f What to Watch Out For:<\/h3>\n\n\n\n
      \n
    • If a line is straight but does not pass through the origin<\/strong>, it is not<\/strong> a direct variation.<\/li>\n\n\n\n
    • Curved lines (like parabolas or circles) never represent direct variation.<\/li>\n\n\n\n
    • If the line has a break, gap, or undefined parts (like a vertical line), it is not a function<\/strong>.<\/li>\n<\/ul>\n\n\n\n
      \n\n\n\n

      \u2705 Summary:<\/h3>\n\n\n\n

      To identify the graph of a function with direct variation:<\/p>\n\n\n\n

        \n
      • Look for a straight line.<\/li>\n\n\n\n
      • Confirm that it goes through (0, 0).
        If both conditions are true, the graph does<\/strong> represent a direct variation.<\/li>\n<\/ul>\n\n\n\n
        \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

        ‘Which graph represents a function with direct variation The Correct Answer and Explanation is: \u2705 Correct Answer: A graph that is a straight line passing through the origin (0, 0) represents a function with direct variation. \ud83d\udcd8 Explanation A direct variation is a type of linear relationship between two variables where one variable is a […]<\/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-228567","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228567","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=228567"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/228567\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=228567"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=228567"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=228567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}