Does the data represent a direct variation or an inverse variation? Write the equation for this data.

Question

(0.5, 100), (2.5, 20), (10, 5)

Answer 1

In a direct variation, the y values increase as the x values increase. That is not the case here - the y values are going down as the x values get larger, so an inverse variation would be appropriate. Try:

y = k/x

Solving for k:

yx = k

The equation could be y = k/x² or some other power of x. But if we plug in all three (x,y) combinations and get the same value for k, we know y=k/x is right.

yx = k

(100)(0.5) = 50

(20)(2.5) = 50

(5)(10) = 50

So yep, k = 50 and the equation is y = 50/x.