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

C

Step-by-step 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