{"id":3494,"date":"2022-02-05T20:26:58","date_gmt":"2022-02-05T20:26:58","guid":{"rendered":"https:\/\/oryxlearning.com\/company\/?page_id=3494"},"modified":"2022-02-05T20:26:58","modified_gmt":"2022-02-05T20:26:58","slug":"what-is-the-constant-of-proportionality","status":"publish","type":"page","link":"https:\/\/oryxlearning.com\/learn\/what-is-the-constant-of-proportionality\/","title":{"rendered":"What is the Constant of Proportionality"},"content":{"rendered":"[vc_section full_width=&#8221;stretch_row&#8221; content_placement=&#8221;middle&#8221; css=&#8221;.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}&#8221; el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text]\n<h5>What is the Constant of Proportionality<\/h5>\n[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of proportionality when, either their ratio or their product yields a constant. The value of the constant of proportionality depends on the type of proportion between the two given quantities: Direct Variation and Inverse Variation.<br \/>\n<strong>Direct Variation:<\/strong> The equation for direct proportionality is <strong>y = kx<\/strong>, which shows as <strong>x<\/strong> increases, <strong>y<\/strong> also increases at the same rate.<br \/>\n<strong>Inverse Variation:<\/strong> The equation for the indirect proportionality is <strong>y =<\/strong> <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{k}{x}\" alt=\"\\fn_phv \\frac{k}{x}\" align=\"absmiddle\" \/>, which shows that as <strong>y<\/strong> increases, <strong>x<\/strong> decreases and vice-versa.<br \/>\nIn both the cases, <strong>k<\/strong> is constant. The value of this constant is called the coefficient of proportionality. The constant of proportionality is also known as <strong>unit rate<\/strong>.[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Rules[\/vc_column_text][vc_column_text]1. In a <a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/direct-variation\">direct variation<\/a> equation, the constant rate of change, or slope, is assigned a special variable, <strong>k<\/strong>.<br \/>\n2. Direct variation can be represented by the equation: <strong>y = kx<\/strong>, where <strong>k \u2260 0<\/strong><br \/>\n3. When a relationship varies directly, the graph of the function will always go through the origin (0,0).[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Example[\/vc_column_text][vc_column_text]<strong><span style=\"color: #16a085;\">Determine if the linear relationship is a direct variation. If so, state the constant of proportionality.<\/span><\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/direct-variation\"><img loading=\"lazy\" class=\"alignnone wp-image-3496 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/11-22.png\" alt=\"\" width=\"271\" height=\"130\" \/><\/a><br \/>\n[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Solution[\/vc_column_text][vc_column_text]The function shows the relationship between the number of apples(<strong>x<\/strong>) and the total cost (<strong>y<\/strong>). Use the direct variation equation to see if the relationship is a direct variation.<br \/>\n<img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{2}{5}=\\frac{2}{5}\" alt=\"\\fn_phv \\frac{2}{5}=\\frac{2}{5}\" align=\"absmiddle\" \/> \u00a0 <img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{4}{10}=\\frac{2}{5}\" alt=\"\\fn_phv \\frac{4}{10}=\\frac{2}{5}\" align=\"absmiddle\" \/>\u00a0 \u00a0 <img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;\\frac{6}{15}=\\frac{2}{5}\" alt=\"\\fn_phv \\frac{6}{15}=\\frac{2}{5}\" align=\"absmiddle\" \/><br \/>\nCompare to the direct variation equation:<br \/>\n<strong><img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;y=\\frac{2}{5}x\" alt=\"\\fn_phv y=\\frac{2}{5}x\" align=\"absmiddle\" \/> to <img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;k=\\frac{2}{5}\" alt=\"\\fn_phv k=\\frac{2}{5}\" align=\"absmiddle\" \/><\/strong><br \/>\n<strong><span style=\"color: red;\">Ans: Yes, <img src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;{\\color{Red}&amp;space;k=\\frac{2}{5}}\" alt=\"\\fn_phv {\\color{Red} k=\\frac{2}{5}}\" align=\"absmiddle\" \/><\/span><\/strong>[\/vc_column_text][vc_column_text el_class=&#8221;headingnew&#8221;]Practice What is the Constant of Proportionality[\/vc_column_text][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 1<\/h5>\n<p><strong><span style=\"color: #16a085;\">Determine if the equation is a direct variation. If so, state the constant of variation.<br \/>\n<\/span><\/strong><img style=\"margin-top: 10px; margin-bottom: 10px;\" src=\"https:\/\/latex.codecogs.com\/svg.latex?\\fn_phv&amp;space;y=\\frac{1}{2}x\" alt=\"\\fn_phv y=\\frac{1}{2}x\" align=\"absmiddle\" \/><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/direct-variation\"><img loading=\"lazy\" class=\"alignnone wp-image-3499 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/111-5.png\" alt=\"\" width=\"256\" height=\"269\" \/><\/a>[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/direct-variation&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=&#8221;30px&#8221;][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 2<\/h5>\n<p><strong><span style=\"color: #16a085;\">Determine if the linear relationship is a direct variation. If so, state the constant of proportionality.<\/span><\/strong><br \/>\n<strong>Write your answer as a whole number or a reduced fraction.<\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-\"><img loading=\"lazy\" class=\"alignnone wp-image-3502 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/12-14.png\" alt=\"\" width=\"213\" height=\"297\" \/><\/a>[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-&#8220;][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=&#8221;30px&#8221;][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 3<\/h5>\n<p><strong><span style=\"color: #16a085;\">Write the direct variation equation that models the situation.<\/span><\/strong><br \/>\n<strong>Jerome builds gift boxes. He builds 5 boxes in 24 seconds. After 38.4 seconds, he has 8 boxes.<br \/>\nx = boxes and y = seconds<\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/direct-variation\"><img loading=\"lazy\" class=\"alignnone wp-image-3504 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/13-14.png\" alt=\"\" width=\"135\" height=\"43\" \/><\/a>[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/direct-variation&#8221;][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=&#8221;30px&#8221;][vc_row_inner el_class=&#8221;boxxborder&#8221;][vc_column_inner][vc_column_text]\n<h5 style=\"margin-bottom: 10px;\">Practice Problem 4<\/h5>\n<p><strong><span style=\"color: #16a085;\">y varies directly with x. Find the value of the variable.<\/span><\/strong><br \/>\n<strong>y = 910 when x = 5. Find x when y = 546<\/strong><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-\"><img loading=\"lazy\" class=\"alignnone wp-image-3506 size-full\" style=\"margin-top: 10px;\" src=\"https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/14-7.png\" alt=\"\" width=\"122\" height=\"45\" \/><\/a>[\/vc_column_text][vc_single_image image=&#8221;2159&#8243; img_size=&#8221;full&#8221; alignment=&#8221;right&#8221; onclick=&#8221;custom_link&#8221; link=&#8221;https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/direct-variation-equations-y-mx-&#8220;][\/vc_column_inner][\/vc_row_inner][vc_empty_space height=&#8221;30px&#8221;][\/vc_column][vc_column width=&#8221;1\/3&#8243; css=&#8221;.vc_custom_1633369011398{margin-bottom: 50px !important;}&#8221;][vc_row_inner el_class=&#8221;stickynotee&#8221;][vc_column_inner][vc_single_image image=&#8221;2265&#8243; img_size=&#8221;full&#8221; alignment=&#8221;center&#8221; css_animation=&#8221;fadeIn&#8221; css=&#8221;.vc_custom_1633509989314{border-radius: 10px !important;}&#8221; el_class=&#8221;stickypin&#8221;][vc_column_text]The <strong>constant of proportionality<\/strong> is the ratio between two directly proportional quantities.<\/p>\n<p><strong>Proportional<\/strong> &#8211; when two quantities have a constant ratio or unit rate.<\/p>\n<p><strong>Direct Variation<\/strong> \u2013 a relationship between two variable quantities with a constant ratio.<\/p>\n<p>A <strong>rate<\/strong> is a ratio that compares two quantities with different kinds of units.<\/p>\n<p>A <strong>unit rate<\/strong> is a rate that is simplified so that it has a denominator of 1 unit.[\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;boxxborder2&#8243;]<span style=\"color: #ed5600;\"><strong>Pre-requisite Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/equivalent-fractions\"><span style=\"color: #ed5600;\">Equivalent Fractions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/5th-grade\/simplifying-fractions\"><span style=\"color: #ed5600;\">Simplifying fractions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/ratio-applications\"><span style=\"color: #ed5600;\">Ratio Applications<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/unit-rate-applications\"><span style=\"color: #ed5600;\">Unit Rate Applications<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/6th-grade\/proportional-relationships-applications\"><span style=\"color: #ed5600;\">Proportional Relationships Applications<\/span><\/a>[\/vc_column_text][vc_column_text el_class=&#8221;boxxborder2&#8243; css=&#8221;.vc_custom_1635254769825{border-top-width: 7px !important;border-right-width: 7px !important;border-bottom-width: 7px !important;border-left-width: 7px !important;background-position: center !important;background-repeat: no-repeat !important;background-size: contain !important;border-left-color: #333399 !important;border-left-style: solid !important;border-right-color: #333399 !important;border-right-style: solid !important;border-top-color: #333399 !important;border-top-style: solid !important;border-bottom-color: #333399 !important;border-bottom-style: solid !important;border-radius: 35px !important;}&#8221;]<span style=\"color: #333399;\"><strong>Related Skills<\/strong><\/span><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/complex-fractions\"><span style=\"color: #333399;\">Complex Fractions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/dimensional-analysis\"><span style=\"color: #333399;\">Dimensional Analysis<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/identifying-proportional-relationships-using-a-table\"><span style=\"color: #333399;\">Identifying Proportional Relationships Using a Table<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/graphing-proportional-relationships\"><span style=\"color: #333399;\">Graphing Proportional Relationships<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/7th-grade\/solving-proportions\"><span style=\"color: #333399;\">Solving Proportions<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/slope-intercept-form-of-an-equation\"><span style=\"color: #333399;\">Slope-intercept Form of an Equation<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/graphing-lines-using-intercepts\"><span style=\"color: #333399;\">Graphing Lines Using Intercepts<\/span><\/a><br \/>\n<a href=\"https:\/\/en.oryxlearning.com\/question\/maths\/8th-grade\/write-linear-equations\"><span style=\"color: #333399;\">Write Linear Equations<\/span><\/a>[\/vc_column_text][vc_row_inner equal_height=&#8221;yes&#8221; 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color=&#8221;vista-blue&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F7th-grade%2Fmaths|title:Grade%207%20Math||&#8221;][vc_btn title=&#8221;Grade 8&#8243; color=&#8221;mulled-wine&#8221; link=&#8221;url:https%3A%2F%2Foryxlearning.com%2Fgrade%2F8th-grade%2Fmaths|title:Grade%208%20Math||&#8221;][\/vc_column_inner][\/vc_row_inner][vc_row_inner equal_height=&#8221;yes&#8221; el_class=&#8221;btninlinespacing&#8221;][vc_column_inner][vc_btn title=&#8221;Algebra&#8221; color=&#8221;warning&#8221; link=&#8221;url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Falgebra|title:Algebra||&#8221;][vc_btn title=&#8221;Fractions&#8221; color=&#8221;danger&#8221; link=&#8221;url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Ffractions|title:Fractions||&#8221;][vc_btn title=&#8221;Ratios and Proportions&#8221; color=&#8221;violet&#8221; link=&#8221;url:https%3A%2F%2Fen.oryxlearning.com%2Ftopics%2Fmaths%2Fratios-and-proportions|title:Ratios%20and%20Proportions||&#8221;][\/vc_column_inner][\/vc_row_inner][\/vc_column][\/vc_row][\/vc_section]\n","protected":false},"excerpt":{"rendered":"<p>[vc_section full_width=&#8221;stretch_row&#8221; content_placement=&#8221;middle&#8221; css=&#8221;.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}&#8221; el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text] What is the Constant of Proportionality [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Constant of proportionality is the constant value of the ratio between two proportional quantities. Two varying quantities are said to be in a relation of [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v17.0 (Yoast SEO v17.6) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>What is the Constant of Proportionality | Oryx Learning<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/oryxlearning.com\/learn\/what-is-the-constant-of-proportionality\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the Constant of Proportionality\" \/>\n<meta property=\"og:description\" content=\"[vc_section full_width=&#8221;stretch_row&#8221; content_placement=&#8221;middle&#8221; css=&#8221;.vc_custom_1633364343825{background-image: url(https:\/\/oryxlearning.com\/learn\/wp-content\/uploads\/2021\/10\/10-min-scaled.jpg?id=2121) !important;background-position: center !important;background-repeat: no-repeat !important;background-size: cover !important;}&#8221; el_id=&#8221;bg-sec&#8221;][vc_row full_width=&#8221;stretch_row_content&#8221; el_class=&#8221;faaaq&#8221;][vc_column width=&#8221;1\/12&#8243;][\/vc_column][vc_column width=&#8221;1\/2&#8243;][vc_row_inner content_placement=&#8221;middle&#8221; el_class=&#8221;topheadingg&#8221;][vc_column_inner width=&#8221;1\/6&#8243;][vc_single_image image=&#8221;2283&#8243; img_size=&#8221;full&#8221;][\/vc_column_inner][vc_column_inner width=&#8221;5\/6&#8243;][vc_column_text] What is the Constant of Proportionality [\/vc_column_text][\/vc_column_inner][\/vc_row_inner][vc_column_text el_class=&#8221;headingnew&#8221;]Concept[\/vc_column_text][vc_column_text]Constant of proportionality is the constant value of the ratio between two proportional quantities. 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