Question

I will give a medal for the best answer (obviously)
For the data in the table, tell whether y varies directly with x.
x y
-6 9
1 -1.5
8 -12

Answer 1

y varies directly with x (or: "x and y are directly proportional") if there is a constant k such that y = kx

9 = k(-6)
-1.5 = k(1)
12 = k(8)

If y varies directly with x, then k must equal -1.5

9 = (-1.5)(6) = 9 true.
12 = (-1.5)(8) = 12 true.

So yes y varies directly with x.