{"id":184924,"date":"2025-01-21T18:48:49","date_gmt":"2025-01-21T18:48:49","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=184924"},"modified":"2025-01-21T18:48:51","modified_gmt":"2025-01-21T18:48:51","slug":"en-vision-algebra-2-name-pearsonrealize","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/21\/en-vision-algebra-2-name-pearsonrealize\/","title":{"rendered":"en Vision Algebra 2 Name PearsonRealize"},"content":{"rendered":"\n

en Vision Algebra 2 Name PearsonRealize.com 4-1 Additional Practice Inverse Variation and the Reciprocal Function Do the tables below represent a direct variation or an inverse variation?<\/p>\n\n\n\n

The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine whether the tables represent a direct variation<\/strong> or an inverse variation<\/strong>, let’s first define both terms:<\/p>\n\n\n\n

Definitions:<\/h3>\n\n\n\n
    \n
  1. Direct Variation<\/strong>: A relationship where two variables xx and yy are proportional, meaning y=kxy = kx, where kk is a constant. In this case, as xx increases, yy increases (or both decrease simultaneously), maintaining the constant ratio yx=k\\frac{y}{x} = k.<\/li>\n\n\n\n
  2. Inverse Variation<\/strong>: A relationship where the product of two variables xx and yy is constant, meaning xy=kxy = k or y=kxy = \\frac{k}{x}. Here, as xx increases, yy decreases, and vice versa, maintaining the constant product xy=kxy = k.<\/li>\n<\/ol>\n\n\n\n
    \n\n\n\n

    Step-by-step Analysis:<\/h3>\n\n\n\n

    To analyze the tables:<\/p>\n\n\n\n

      \n
    1. Check if the ratio yx\\frac{y}{x} remains constant (direct variation).<\/li>\n\n\n\n
    2. Check if the product xyxy remains constant (inverse variation).<\/li>\n<\/ol>\n\n\n\n

      Example Table:<\/h4>\n\n\n\n
      xx<\/th>yy<\/th><\/tr><\/thead>
      1<\/td>12<\/td><\/tr>
      2<\/td>6<\/td><\/tr>
      3<\/td>4<\/td><\/tr>
      4<\/td>3<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n

      Testing for Direct Variation:<\/h4>\n\n\n\n
        \n
      • Compute yx\\frac{y}{x}: 121=12,62=3,43\u2260constant\\frac{12}{1} = 12, \\quad \\frac{6}{2} = 3, \\quad \\frac{4}{3} \\neq \\text{constant}<\/li>\n\n\n\n
      • The ratio yx\\frac{y}{x} is not constant, so not a direct variation<\/strong>.<\/li>\n<\/ul>\n\n\n\n

        Testing for Inverse Variation:<\/h4>\n\n\n\n
          \n
        • Compute xyxy: 1\u22c512=12,2\u22c56=12,3\u22c54=12,4\u22c53=121 \\cdot 12 = 12, \\quad 2 \\cdot 6 = 12, \\quad 3 \\cdot 4 = 12, \\quad 4 \\cdot 3 = 12<\/li>\n\n\n\n
        • The product xyxy is constant, so this is an inverse variation<\/strong>.<\/li>\n<\/ul>\n\n\n\n
          \n\n\n\n

          Explanation :<\/h3>\n\n\n\n

          A table represents direct variation<\/strong> if the ratio yx\\frac{y}{x} is constant, meaning yy increases or decreases proportionally with xx. For example, if x=1,2,3x = 1, 2, 3 and y=2,4,6y = 2, 4, 6, the ratio yx=2\\frac{y}{x} = 2 remains constant, indicating direct variation.<\/p>\n\n\n\n

          In contrast, a table represents inverse variation<\/strong> if the product xyxy is constant. This relationship implies that as xx increases, yy decreases, and vice versa. For instance, if x=1,2,4x = 1, 2, 4 and y=8,4,2y = 8, 4, 2, the product xy=8xy = 8 remains the same.<\/p>\n\n\n\n

          To determine the type of variation, analyze the given data. Calculate yx\\frac{y}{x} for all pairs in the table. If constant, it is a direct variation. Otherwise, compute xyxy; if constant, it is an inverse variation. If neither is constant, the table does not represent either type of variation.<\/p>\n\n\n\n

          For example, in the table where x=1,2,3,4x = 1, 2, 3, 4 and y=12,6,4,3y = 12, 6, 4, 3, the ratio yx\\frac{y}{x} varies (12, 3, etc.), eliminating direct variation. However, the product xy=12xy = 12 for all entries, confirming inverse variation.<\/p>\n\n\n\n

          Understanding these patterns helps identify relationships between variables, providing insights into their mathematical behavior.<\/p>\n","protected":false},"excerpt":{"rendered":"

          en Vision Algebra 2 Name PearsonRealize.com 4-1 Additional Practice Inverse Variation and the Reciprocal Function Do the tables below represent a direct variation or an inverse variation? The correct answer and explanation is: To determine whether the tables represent a direct variation or an inverse variation, let’s first define both terms: Definitions: Step-by-step Analysis: To […]<\/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-184924","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184924","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=184924"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184924\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=184924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=184924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=184924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}