Question

How do you determine whether `x=14y` is an inverse or direct variation?

Answer 1

By the sign and fraction (if any) applied to the second factor.

Explanation:

A “direct” variation means that as one factor increases or decreases, the other one moves in the same direction. An “inverse” variation means that the second factor moves in the opposite direction from the first factor.

That is, if the first factor increases, the second one decreases. The two ways that an inverse variation can be achieved are by a negative value assignment (-) or a reciprocal fraction – a “`(1/y)`" term.

In this case the second factor (14y) is both positive and directly proportional (no fraction), so this equation shows a direct variation of y with respect to x.

In contrast, x = -14y or x = 14/y would both be inverse variations.