Question

Which of the following are direct variations?

Select all that apply

y = 3x

y=4/x

y = 2x^2

xy = 3

Answer 1

Direct variation means y = kx for some constant k.

- y = 3x — yes (k = 3).
- y = 4/x — no (inverse variation).
- y = 2x^2 — not of the form y = kx (it’s y = kx^2, i.e. “varies directly as x^2,” but not direct variation in x).
- xy = 3 — no (y = 3/x, inverse variation).

So only y = 3x is a direct variation.