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 Question from jennifer: assume that y varies directly as x. find y when x = 54 if y =1/4 when x=3/2

Hi Jennifer.

When we say y varies directly as x, we mean that the ratio between these variables is constant. In fact, if we write the ratio as a fraction (y / x), then we call this fraction the constant of variation. So any fraction that equals this constant is a value pair that satisfies the conditions.

Here is an example. Assume that y varies directly as x. Find y when x = 10 if y = 7.5 when x = 3.

This means we know the constant of variation is 7.5 / 3, which equals 2.5. So any fraction that equals 2.5 satisfies the conditions. Therefore if y / x = 2.5 and x = 10, then y / 10 = 2.5, so y = 2.5  10 = 25.