Answer:
Set (c) pairs all satisfy the equation y = (1/3)x - 1.
Explanation:
We have to evaluate the function y = (1/3)x - 1 at many (but not all) of the given points. If we find even one point in each of the four given sets, we reject that set.
Set (a): Does (0,-1) satisfy y = (1/3)x - 1? Is -1 = (1/3)(0) -1 true? Yes. But move on to the next point in this set, (-3,0), before celebrating. Does (-3,0) satisfy y = (1/3)x - 1? Is 0 = (1/3)(-3) -1 true? Is 0 = -1 -1 true? NO. Reject set (a).
Set (b): Does (3,0) satisfy y = (1/3)x - 1? Is 0 = (1/3)(3) - 1 true? Yes. Keep going ...try (0,-1). Does (0, -1) satisfy y = (1/3)x - 1? Is -1 = (1/3)(0) -1 true? Yes. Keep going. Does (6, 1) satisfy y = (1/3)x - 1? Is 1 = (1/3)(6) - 1 true? Yes.
Set (b) contains ordered pairs for y = (1/3)x - 1.
We must do the same thing for sets (c) and (d).
I used my calculator for (c). The second ordered pair in (c) fails. Reject (c).
The first two pairs of (d) fail, but (6,1) is OK. But we must reject the entire set (d).