Some textbooks describe direct variation by saying " y varies directly as x ", " y varies proportionally as x ", or " y is directly proportional to x. This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same. Direct Variation Equation. Substitute the given x and y values, and solve for k. From the graph we can see whether the value of k is positive or negative. Find the constant of variation and the slope of the model.
To find the slope, we use the slope formula:. We confirm with the answer that k is the slope of the graph. Writing a Direct Variation Equation. Write an equation that relates x and y. We can then solve for k by using the given values for x and y. To find the value of y , we substitute for x. This means that as x increases, y decreases and as x decreases, y increases. The graph of the inverse variation equation is a hyperbola. Inverse Variation Equation for 3 different values of k.
Names of standardized tests are owned by the trademark holders and are not affiliated with Varsity Tutors LLC. Show Solution Check. Related Lessons. Joint Variation and Combined Variation - Definitions. View All Related Lessons. Anusha Rahman. Direct Variation We can use direct variation to describe a specific type of relationship between two variables.
If we want to mathematically graph these numbers, there's an equation for it! Image source: by Anusha Rahman. Direct Variation In algebra, we will see direct variation, inverse variation , and joint variation. Let's look at an example. First, let's solve for k.
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