Inverse Variation Equations

Definition: In an inverse variation, the values of the two variables change in an opposite manner – as one value increases, the other decreases. It is said that one variable varies inversely as the other. The formula for inverse variation is y = k/x, where k is the constant of variation.

Example: If y varies inversely as x and x=7 when y=5, find the variation equation.

Solution:

Step 1: Substitute the x and y into the equation. This gives us: 5 = k/7.

Step 2: Solve the equation for k. In this example, we multiply both sides by 7 to yield: k = 35.

Step 3: Rewrite the original formula with just the k plugged in: y = 35/x.

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