Determine the constant of variation for the direct variation given

(0.0), (3, 12). (9. 36)

3

4

12

The const. of variation / proportionality is thus 4.

Step-by-step explanation:

Direct variation is modeled by y = kx, where k is the constant of proportionality. The associated line passes thru the origin, and so the y-intercept, b, is zero.

If we go from (3, 12) to (9, 36), x increases by 6 and y increases by 24. Thus, the slope, same as the constant of proportionality in this case, is

k = rise / run = 24 / 6, or 4. The const. of variation / proportionality is thus 4.