{"id":33196,"date":"2023-08-18T18:10:54","date_gmt":"2023-08-18T18:10:54","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=33196"},"modified":"2023-08-19T19:19:29","modified_gmt":"2023-08-19T19:19:29","slug":"direct-variation-definition-formula-equation-examples-faqs","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation","title":{"rendered":"Direct Variation: Definition, Formula, Equation, Examples, FAQs"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-538bbbea-5ff3-4cf3-b36c-8fb45f6e3021\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation#0-what-is-direct-variation-in-math>What Is Direct Variation in Math?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation#3-what-is-a-direct-variation-equation-direct-variation-formula>What Is a Direct Variation Equation? (Direct Variation Formula)<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation#6-difference-between-direct-variation-and-inverse-variation>Difference between Direct Variation and Inverse Variation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation#9-solved-examples-of-direct-variation>Solved Examples of Direct Variation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation#10-practice-problems-on-direct-variation>Practice Problems on Direct Variation<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation#11-frequently-asked-questions-about-direct-variation>Frequently Asked Questions about Direct Variation<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-direct-variation-in-math\">What Is Direct Variation in Math?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Direct variation is a type of proportionality in which one quantity directly varies with respect to a change in another quantity, by the same factor.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This means that an increase in one quantity results in a proportionate increase in the other quantity. Similarly, a decrease in one quantity results in a proportionate decrease in the other quantity. There will be a proportionate increase or decrease.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Note that the ratio between two quantities that are in direct proportion or direct variation always remains the same.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In direct variation, the variable that represents the cause of the relationship is called the independent variable, generally denoted by x. The other variable depends on the value of the independent variable; it is called the dependent variable, generally denoted by y.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">(<strong>Note: <\/strong>It\u2019s important to note that the roles of independent and dependent variables vary depending on the specific context and the relationship between the defined variables. It is always better to first understand the relationship between two quantities in comparison.)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Direct variation real-life example:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose you are working on an hourly pay basis. In this case, the number of hours you work is directly proportional to your earnings. The more you work, the more you earn. You can earn double by working twice as many hours.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, $x =$ Number of hours you work and $y =$ The amount of money you earn<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"423\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-direct-variation.png\" alt=\"Number of hours and amount of money - direct variation\" class=\"wp-image-33233\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-direct-variation.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/example-of-direct-variation-300x205.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"1-direct-variation-definition\">Direct Variation Definition<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Direct variation or direct proportionality is a mathematical relationship between two variables where one variable varies in direct proportion with respect to the other variable.<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-direct-variation-symbol\">Direct Variation Symbol<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose that a variable y is directly proportional to x. In other words, y varies directly as x.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We can write this mathematically as<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$y \\propto x$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Symbol \u201c$\\propto$\u201d stands for \u201cis proportional to.\u201d<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-what-is-a-direct-variation-equation-direct-variation-formula\">What Is a Direct Variation Equation? (Direct Variation Formula)<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The relationship between two variables x and y, which are in direct variation, can be represented by an equation<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$y = kx$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$k = \\frac{y}{x}$ is the constant of variation representing the constant ratio between the two variables.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Here, k is a non-zero real constant. The value of k can be both positive or negative.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The above equation can be decoded as \u201cy varies directly with x\u201d or \u201cy varies directly as x.\u201d The equation can be used to derive different formulas according to the requirements of a solution.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Different forms of the direct variation formula are as follows:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To solve for the constant of variation, k, we can shuffle the formula.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">$k = \\frac{y}{x}$ and $x \\neq 0$<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>To solve for one of the variables (x or y), we can shuffle the formula.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">$y = kx$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">or<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$x = \\frac{y}{k}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-direct-variation-on-a-graph\">Direct Variation on a Graph<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Note that the graph of the direct variation linear equation <\/strong>$y = kx$<strong> is a straight line passing through the origin.<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>If k is positive, then the line will rise from left to right, passing through the origin.<\/li>\n\n\n\n<li>If k is negative, then the line will fall from left to right, passing through the origin.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The slope of the line represents the constant of variation in a direct variation. It indicates how much the dependent variable changes for each unit increase in the independent variable.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, to understand how to graph direct variation, we will identify the plot points satisfying the equation $y = kx$.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"494\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/direct-variation-graph.png\" alt=\"Direct Variation showing a Linear Graph passing through the Origin (0, 0)\" class=\"wp-image-33235\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/direct-variation-graph.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/direct-variation-graph-300x239.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-cross-multiplication-method-to-solve-direct-variation-problems\">Cross Multiplication Method to Solve Direct Variation Problems<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">We can easily solve direct variation problems using the cross multiplication method. Consider two variables, x and y, in direct variation.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let y = B for x = A.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let y = D for x = C.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Since x and y are in direct variation, we can write the proportion as<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\frac{A}{B} = \\frac{C}{D}$\u00a0<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">By cross multiplication, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, $A \\times D = B \\times C$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We can find any missing value using this method.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"565\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/direct-variation-and-cross-multiplication.png\" alt=\"Cross multiplication shortcut for direct variation problems\" class=\"wp-image-33236\" title=\"Cross multiplication shortcut for direct variation problems\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/direct-variation-and-cross-multiplication.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/direct-variation-and-cross-multiplication-300x273.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-difference-between-direct-variation-and-inverse-variation\">Difference between Direct Variation and Inverse Variation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In a direct variation, the variables change in proportion to each other, while in an inverse variation, the variables change in inverse proportion to each other.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">See this comparison table that shows the difference between Direct and Inverse variations:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th><strong>Feature<\/strong><\/th><th><strong>Direct Variation<\/strong><\/th><th><strong>Inverse Variation<\/strong><\/th><\/tr><\/thead><tbody><tr><td>Definition<\/td><td>One variable varies in direct proportion with respect to the other variable.<\/td><td>One variable varies in inverse proportion with respect to the other variable<\/td><\/tr><tr><td>Meaning<\/td><td>As x increases, y increases by the same factor. As x decreases, y decreases by the same factor.<\/td><td>As x increases, y decreases by the same factor. As x decreases, y increases by the same factor.<\/td><\/tr><tr><td>Equation<\/td><td>$y = kx$<\/td><td>$y = \\frac{k}{x}$<\/td><\/tr><tr><td>Symbol<\/td><td>$x \\propto y$<br>x \u201cis directly proportional to\u201d y.<\/td><td>$x \\propto \\frac{1}{y}$<br>x \u201cis inversely proportional to\u201d y.<\/td><\/tr><tr><td>Constant of Variation<\/td><td>$k = \\frac{y}{x}$<\/td><td>$k = xy$<\/td><\/tr><tr><td>Graph<\/td><td>The graph is a straight line that passes through the origin.<br><img loading=\"lazy\" decoding=\"async\" width=\"170\" height=\"157\" class=\"wp-image-33226\" style=\"width: 170px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-direct-variation.png\" alt=\"Graph of direct variation\"><\/td><td>The plot is a hyperbola with two branches.<br><img loading=\"lazy\" decoding=\"async\" width=\"170\" height=\"158\" class=\"wp-image-33227\" style=\"width: 170px;\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/graph-of-inverse-proportion.png\" alt=\"Graph of inverse proportion\"><\/td><\/tr><tr><td>Examples<\/td><td>The cost of items is directly proportional to the number of items.<\/td><td>The speed of an object is inversely proportional to the time taken.<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-facts-on-direct-variation\">Facts on Direct Variation<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>The constant of variation (k) is the fixed ratio that does not change even if the values of x and y change.<\/li>\n\n\n\n<li>The graph line passes through the origin (0,0) because the direct variation equation always includes the term y = 0 when x = 0.<\/li>\n\n\n\n<li>The constant of variation (k) gets bigger with a rise in the steepness of the slope of the line.<\/li>\n\n\n\n<li>A horizontal graph line indicates that the variable y is constant and does not change with x; hence, it does not have direct variation.<\/li>\n\n\n\n<li>A vertical graph line indicates that the variable x is constant and does not change with y; hence, it does not have direct variation.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Okay, so we now have a clear idea of the concepts relating to direct variation, including direct variation function, definition, graph, differences, and much more. Let us now look at some examples and practice problems to boost our understanding of the concept.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-solved-examples-of-direct-variation\">Solved Examples of Direct Variation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. The cost of printing 100 pages is $50. What will be the cost of printing 150 pages?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cost $\\propto$ Number of pages<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cost $= k \\times$ Number of pages<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$k = \\frac{y}{x} = \\frac{cost}{Number \\;of \\;pages}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$k = \\frac{50}{100} = 0.5$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, the cost of 150 pages can be calculated by a direct variation equation.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cost $= 0.5 \\times $Number of pages<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cost $= 0.5 \\times 150$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cost $= 75$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, $\\$75$ is the cost of printing 150 pages.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Another method:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Cost<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Number of pages<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">$\\$50$<\/td><td class=\"has-text-align-left\" data-align=\"left\">100<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">?<\/td><td class=\"has-text-align-left\" data-align=\"left\">150<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">By cross multiplication, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\$50 \\times 150 = 100 \\times$ ?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">?$ = \\frac{\\$7500}{100}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">? $= \\$75$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. If the number and cost of notebooks have a direct variation, what will be the cost of 15 notebooks if 5 notebooks cost <\/strong>$\\$10$<strong>?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As the cost varies directly with the number of notebooks, we can solve it by setting up the proportions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">5 notebooks cost $\\$10$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let the cost of 15 notebooks to be x.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The proportion can be written as<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\frac{5}{10} = \\frac{15}{x}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cross multiply.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$5 \\times x = 10 \\times 15$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Solve for x<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$x = 30$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, $\\$30$ is the cost of 15 notebooks.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. If a car covers 240 miles in 4 hours time. How many miles will it travel in 6 hours?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">We know that the distance covered is directly proportional to the time taken. So, we can solve this question accordingly.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Distance covered<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Time taken<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">240 miles<\/td><td class=\"has-text-align-left\" data-align=\"left\">4 hours<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>?<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">6 hours<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">By cross multiplication, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">240 miles$\\times 6 =$ ?$\\times 4$ hours<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">?$= 360$ miles<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, the car will cover 360 miles in 6 hours.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. A company produces 100 units of a product per day. How many units will it produce in 5 days?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The number of units produced are directly proportional to the number of days.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Number of units produced<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Number of days<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">100<\/td><td class=\"has-text-align-left\" data-align=\"left\">1<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\"><strong>y = ?<\/strong><\/td><td class=\"has-text-align-left\" data-align=\"left\">5<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Suppose that the company produces y units in 5 days.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">By cross multiplication, we get<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$y = 100 \\times 5$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$y = 500$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, 500 units can be produced in 5 days.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>5. Find the constant of direct variation where the cost of 4 dozen oranges is <\/strong>$\\$24$<strong>. Also, find the cost of 8 dozen oranges.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Assume the cost of 8 dozen oranges to be y.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">As we can see that the cost of oranges varies directly with the number of dozens. So, we can set up a proportion as<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\frac{4}{24} = 8y$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Isolate y on one side by cross-multiplying both sides<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$4y = 24 \\times 8$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Simplify it<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$4y = 192$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$y = 48$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, 8 dozen oranges will cost $48.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Now, let us find the constant of direct variation by using the equation y = kx<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">where&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">y = the cost,<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x = the number of dozens, and<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">k = the constant of variation<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$k = \\frac{1}{6}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, $\\frac{1}{6}$ or 0.1667 (approx) is the constant of direct variation.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-practice-problems-on-direct-variation\">Practice Problems on Direct Variation<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Direct Variation: Definition, Formula, Equation, Examples, FAQs<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">What will be the cost of 10 donuts if 4 donuts cost $\\$2$?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\$2.50$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\$5$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\$4$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\$8$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\$5$<br\/>4 donuts cost $\\$2$. How much will 10 donuts cost?<br>\r\n$\\frac{4}{2} = \\frac{10}{x}$<br>\r\n$x = 5$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">If it takes 2 hours to mow a 1 acre lawn, how many hours will it take to mow a lawn that is $\\frac{1}{4}$ an acre?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">4 hours<\/div><div class=\"spq_answer_block\" data-value=\"1\">2 hours<\/div><div class=\"spq_answer_block\" data-value=\"2\">16 hours<\/div><div class=\"spq_answer_block\" data-value=\"3\">8 hours<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 8 hours<br\/>It takes 2 hours to mow a 1 acre lawn. Let the number of hours taken to mow $\\frac{1}{4} = 0.25$ acre lawn be x.<br>\r\n$\\frac{2}{0.25} = \\frac{x}{1}$<br>\r\n$x = 8$ hours.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">If a car can go 30 miles with one gallon of gas, then how far can it go with 6 gallons of gas?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">5 miles<\/div><div class=\"spq_answer_block\" data-value=\"1\">60 miles<\/div><div class=\"spq_answer_block\" data-value=\"2\">30 miles<\/div><div class=\"spq_answer_block\" data-value=\"3\">180 miles<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 180 miles<br\/>A car goes 30 miles with 1 gallon of gas. Suppose that it can travel x miles with 6 gallons of gas.<br>\r\n$\\frac{1}{30} = \\frac{6}{x}$<br>\r\n$x = 180$ miles<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">5 pounds of apples cost $\\$10$. What will be the cost of 8.5 pounds of apples?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$\\$20$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$\\$17$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\$23$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$\\$21.25$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $\\$21.25$<br\/>5 pounds of apples cost $\\$10$.<br>\r\nLet 8.5 pounds of apples cost $\\$x$.<br>\r\n$\\frac{10}{5} = \\frac{x}{8.5}$<br>\r\n$x = 17$<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Which equation represents a direct variation?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$y = \\frac{1}{x}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$y = 3x$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$y = 2x + 1$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$y = x^{-1}$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $y = 3x$<br\/>The equation $y = 3x$ represents a direct variation because y is directly proportional to x with a constant of proportionality 3. The other options do not represent direct variations as they do not have a constant ratio between the two variables. <\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Direct Variation: Definition, Formula, Equation, Examples, FAQs\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Direct Variation\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"What will be the cost of 10 donuts if 4 donuts cost $$\\\\$$2$$?\",\n                    \"text\": \"What will be the cost of 10 donuts if 4 donuts cost $$\\\\$$2$$?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"4 donuts cost $$\\\\$$2$$. How much will 10 donuts cost?<br>\r\n$$\\\\frac{4}{2} = \\\\frac{10}{x}$$<br>\r\n$$x = 5$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$2.50$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"4 donuts cost $$\\\\$$2$$. How much will 10 donuts cost?<br>\r\n$$\\\\frac{4}{2} = \\\\frac{10}{x}$$<br>\r\n$$x = 5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$4$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"4 donuts cost $$\\\\$$2$$. How much will 10 donuts cost?<br>\r\n$$\\\\frac{4}{2} = \\\\frac{10}{x}$$<br>\r\n$$x = 5$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$8$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"4 donuts cost $$\\\\$$2$$. 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How much will 10 donuts cost?<br>\r\n$$\\\\frac{4}{2} = \\\\frac{10}{x}$$<br>\r\n$$x = 5$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If it takes 2 hours to mow a 1 acre lawn, how many hours will it take to mow a lawn that is $$\\\\frac{1}{4}$$ an acre?\",\n                    \"text\": \"If it takes 2 hours to mow a 1 acre lawn, how many hours will it take to mow a lawn that is $$\\\\frac{1}{4}$$ an acre?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"It takes 2 hours to mow a 1 acre lawn. Let the number of hours taken to mow $$\\\\frac{1}{4} = 0.25$$ acre lawn be x.<br>\r\n$$\\\\frac{2}{0.25} = \\\\frac{x}{1}$$<br>\r\n$$x = 8$$ hours.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"4 hours\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It takes 2 hours to mow a 1 acre lawn. Let the number of hours taken to mow $$\\\\frac{1}{4} = 0.25$$ acre lawn be x.<br>\r\n$$\\\\frac{2}{0.25} = \\\\frac{x}{1}$$<br>\r\n$$x = 8$$ hours.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 hours\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It takes 2 hours to mow a 1 acre lawn. Let the number of hours taken to mow $$\\\\frac{1}{4} = 0.25$$ acre lawn be x.<br>\r\n$$\\\\frac{2}{0.25} = \\\\frac{x}{1}$$<br>\r\n$$x = 8$$ hours.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"16 hours\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"It takes 2 hours to mow a 1 acre lawn. Let the number of hours taken to mow $$\\\\frac{1}{4} = 0.25$$ acre lawn be x.<br>\r\n$$\\\\frac{2}{0.25} = \\\\frac{x}{1}$$<br>\r\n$$x = 8$$ hours.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"8 hours\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"It takes 2 hours to mow a 1 acre lawn. Let the number of hours taken to mow $$\\\\frac{1}{4} = 0.25$$ acre lawn be x.<br>\r\n$$\\\\frac{2}{0.25} = \\\\frac{x}{1}$$<br>\r\n$$x = 8$$ hours.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"It takes 2 hours to mow a 1 acre lawn. Let the number of hours taken to mow $$\\\\frac{1}{4} = 0.25$$ acre lawn be x.<br>\r\n$$\\\\frac{2}{0.25} = \\\\frac{x}{1}$$<br>\r\n$$x = 8$$ hours.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"If a car can go 30 miles with one gallon of gas, then how far can it go with 6 gallons of gas?\",\n                    \"text\": \"If a car can go 30 miles with one gallon of gas, then how far can it go with 6 gallons of gas?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"A car goes 30 miles with 1 gallon of gas. Suppose that it can travel x miles with 6 gallons of gas.<br>\r\n$$\\\\frac{1}{30} = \\\\frac{6}{x}$$<br>\r\n$$x = 180$$ miles\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"5 miles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A car goes 30 miles with 1 gallon of gas. Suppose that it can travel x miles with 6 gallons of gas.<br>\r\n$$\\\\frac{1}{30} = \\\\frac{6}{x}$$<br>\r\n$$x = 180$$ miles\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"60 miles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A car goes 30 miles with 1 gallon of gas. Suppose that it can travel x miles with 6 gallons of gas.<br>\r\n$$\\\\frac{1}{30} = \\\\frac{6}{x}$$<br>\r\n$$x = 180$$ miles\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"30 miles\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"A car goes 30 miles with 1 gallon of gas. Suppose that it can travel x miles with 6 gallons of gas.<br>\r\n$$\\\\frac{1}{30} = \\\\frac{6}{x}$$<br>\r\n$$x = 180$$ miles\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"180 miles\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"A car goes 30 miles with 1 gallon of gas. Suppose that it can travel x miles with 6 gallons of gas.<br>\r\n$$\\\\frac{1}{30} = \\\\frac{6}{x}$$<br>\r\n$$x = 180$$ miles\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"A car goes 30 miles with 1 gallon of gas. Suppose that it can travel x miles with 6 gallons of gas.<br>\r\n$$\\\\frac{1}{30} = \\\\frac{6}{x}$$<br>\r\n$$x = 180$$ miles\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"5 pounds of apples cost $$\\\\$$10$$. What will be the cost of 8.5 pounds of apples?\",\n                    \"text\": \"5 pounds of apples cost $$\\\\$$10$$. What will be the cost of 8.5 pounds of apples?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"5 pounds of apples cost $$\\\\$$10$$.<br>\r\nLet 8.5 pounds of apples cost $$\\\\$$x$$.<br>\r\n$$\\\\frac{10}{5} = \\\\frac{x}{8.5}$$<br>\r\n$$x = 17$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$20$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 pounds of apples cost $$\\\\$$10$$.<br>\r\nLet 8.5 pounds of apples cost $$\\\\$$x$$.<br>\r\n$$\\\\frac{10}{5} = \\\\frac{x}{8.5}$$<br>\r\n$$x = 17$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$17$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 pounds of apples cost $$\\\\$$10$$.<br>\r\nLet 8.5 pounds of apples cost $$\\\\$$x$$.<br>\r\n$$\\\\frac{10}{5} = \\\\frac{x}{8.5}$$<br>\r\n$$x = 17$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\$$23$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"5 pounds of apples cost $$\\\\$$10$$.<br>\r\nLet 8.5 pounds of apples cost $$\\\\$$x$$.<br>\r\n$$\\\\frac{10}{5} = \\\\frac{x}{8.5}$$<br>\r\n$$x = 17$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$\\\\$$21.25$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"5 pounds of apples cost $$\\\\$$10$$.<br>\r\nLet 8.5 pounds of apples cost $$\\\\$$x$$.<br>\r\n$$\\\\frac{10}{5} = \\\\frac{x}{8.5}$$<br>\r\n$$x = 17$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"5 pounds of apples cost $$\\\\$$10$$.<br>\r\nLet 8.5 pounds of apples cost $$\\\\$$x$$.<br>\r\n$$\\\\frac{10}{5} = \\\\frac{x}{8.5}$$<br>\r\n$$x = 17$$\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Which equation represents a direct variation?\",\n                    \"text\": \"Which equation represents a direct variation?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The equation $$y = 3x$$ represents a direct variation because y is directly proportional to x with a constant of proportionality 3. The other options do not represent direct variations as they do not have a constant ratio between the two variables. \"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y = \\\\frac{1}{x}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation $$y = 3x$$ represents a direct variation because y is directly proportional to x with a constant of proportionality 3. The other options do not represent direct variations as they do not have a constant ratio between the two variables. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y = 2x + 1$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation $$y = 3x$$ represents a direct variation because y is directly proportional to x with a constant of proportionality 3. The other options do not represent direct variations as they do not have a constant ratio between the two variables. \"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$y = x^{-1}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The equation $$y = 3x$$ represents a direct variation because y is directly proportional to x with a constant of proportionality 3. The other options do not represent direct variations as they do not have a constant ratio between the two variables. \"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$y = 3x$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The equation $$y = 3x$$ represents a direct variation because y is directly proportional to x with a constant of proportionality 3. The other options do not represent direct variations as they do not have a constant ratio between the two variables. \"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The equation $$y = 3x$$ represents a direct variation because y is directly proportional to x with a constant of proportionality 3. The other options do not represent direct variations as they do not have a constant ratio between the two variables. \"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-frequently-asked-questions-about-direct-variation\">Frequently Asked Questions about Direct Variation<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-85732e45-a4c4-4157-810a-4ad1236376a2\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-85732e45-a4c4-4157-810a-4ad1236376a2\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-85732e45-a4c4-4157-810a-4ad1236376a2\"><strong>Are the terms direct variation and direct proportion the same?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-85732e45-a4c4-4157-810a-4ad1236376a2\">\n\n<p class=\"wp-block-paragraph\">Yes, the terms direct variation and direct proportion are used interchangeably, but mean the same thing.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-85732e45-a4c4-4157-810a-4ad1236376a2\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-85732e45-a4c4-4157-810a-4ad1236376a2\"><strong>How can you identify direct variation?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-85732e45-a4c4-4157-810a-4ad1236376a2\">\n\n<p class=\"wp-block-paragraph\">In direct variation, the ratio of two quantities is always constant. As one variable increases, the other variable also increases. Also, if one variable decreases, the other variable also decreases.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-85732e45-a4c4-4157-810a-4ad1236376a2\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-85732e45-a4c4-4157-810a-4ad1236376a2\"><strong>Can the constant of proportionality be negative?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-85732e45-a4c4-4157-810a-4ad1236376a2\">\n\n<p class=\"wp-block-paragraph\">Yes, it can be positive or negative. It can never be 0. When we study the positive rate of change, we only consider positive values of k.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-3-85732e45-a4c4-4157-810a-4ad1236376a2\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-85732e45-a4c4-4157-810a-4ad1236376a2\"><strong>Are direct variations always linear?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-3-85732e45-a4c4-4157-810a-4ad1236376a2\">\n\n<p class=\"wp-block-paragraph\">We mostly study direct variations that are linear, but they do not have to be linear. We can say that linear equations are a specific type of direct variation, but not all direct variations follow a linear relationship. In direct variation, the ratio between the two variables remains constant, regardless of the type of relationship they exhibit.<\/p>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is Direct Variation in Math? Direct variation is a type of proportionality in which one quantity directly varies with respect to a change in another quantity, by the same factor.&nbsp; This means that an increase in one quantity results in a proportionate increase in the other quantity. Similarly, a decrease in one quantity results &#8230; <a title=\"Direct Variation: Definition, Formula, Equation, Examples, FAQs\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/direct-variation\" aria-label=\"More on Direct Variation: Definition, Formula, Equation, Examples, FAQs\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-33196","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33196","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=33196"}],"version-history":[{"count":11,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33196\/revisions"}],"predecessor-version":[{"id":36333,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/33196\/revisions\/36333"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=33196"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=33196"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=33196"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}