Definition: When two variable quantities have a constant ratio, their relationship is called a direct variation. It is said that one variable varies directly as the other. The formula for direct variation is y = kx, where k is the constant of variation.
Example: If y varies directly as x and x=7 when y=5, find the variation equation.
Step 1: Substitute the x and y into the equation. This gives us: 5 = 7k.
Step 2: Solve the equation for k. In this example, we divide both sides by 7 to yield: k = 5/7.
Step 3: Rewrite the original formula with just the k plugged in: y = (5/7)x
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