Analyzing Rate of Change: Uniform or Non-Uniform from X-Y Coordinate Table

To determine whether the rate of change is uniform, we calculate the slope between each consecutive pair of points provided in the table:

• Calculate the slope between $(-5, 3)$ and $(0, 2)$:
  - The change in $Y$ is $2 - 3 = -1$.
  - The change in $X$ is $0 - (-5) = 5$.
  - Thus, the slope is $\frac{-1}{5} = -0.2$.
• Calculate the slope between $(0, 2)$ and $(5, 0)$:
  - The change in $Y$ is $0 - 2 = -2$.
  - The change in $X$ is $5 - 0 = 5$.
  - Thus, the slope is $\frac{-2}{5} = -0.4$.
• Calculate the slope between $(5, 0)$ and $(10, -2)$:
  - The change in $Y$ is $-2 - 0 = -2$.
  - The change in $X$ is $10 - 5 = 5$.
  - Thus, the slope is $\frac{-2}{5} = -0.4$.

We observe that the slopes are not all the same: the first slope $-0.2$ differs from the others, which are both $-0.4$. Therefore, the rate of change is not uniform across the intervals.

Thus, the rate of change in the function represented by the table is non-uniform.