Question

Which of the following is an example of direct variation?

A) y= x - 2
B) y= 2(x + 5)
C) x - 3y = 0
D) x= y + 3

Answer 1

C

Explanation:

Direct variation is a special case of first order equations; in both cases, the input is multiplied by a constant which we call the "slope" or "constant of variation." However, no direct variation equation includes a constant ("y-intercept"). So, if a given equation does have a y-intersect, that equation does not represent direct variation; if it does NOT have a y-intercept, that equation represents direct variation.

A) involves a constant term, -2; NOT direct variation

B) involves a constant term, 10; NOT direct variation

C) Here 3y = x, or y = x/3, involves no constant term, so Does represent direct variation

D) involves a constant term -3; NOT direct variation