determine weather the rates of change are constant or variablex -2 0 2 5y -3 -9 -18 -24

To determine whether the rates of change are constant or variable, we need to calculate the rate of change between each pair of points. The rate of change is calculated as the change in y divided by the change in x, or Δy/Δx.

1. Between (-2, -3) and (0, -9): Δy = -9 - (-3) = -6 Δx = 0 - (-2) = 2 Rate of change = Δy/Δx = -6/2 = -3

2. Between (0, -9) and (2, -18): Δy = -18 - (-9) = -9 Δx = 2 - 0 = 2 Rate of change = Δy/Δx = -9/2 = -4.5

3. Between (2, -18) and (5, -24): Δy = -24 - (-18) = -6 Δx = 5 - 2 = 3 Rate of change = Δy/Δx = -6/3 = -2

The rates of change are -3, -4.5, and -2, respectively. Since these rates are not the same, the rate of change is variable, not constant.