Analyzing Rate of Change: Function Table with X-Values 1-4 and Y-Values -6 to 3

To determine if the rate of change is uniform, we need to calculate the slope between each pair of consecutive points and check for consistency.

Let's compute the slopes:

• Between $(1, -6)$ and $(2, -3)$:
  $\Delta y = -3 - (-6) = 3$
  $\Delta x = 2 - 1 = 1$
  Slope $= \frac{3}{1} = 3$
• Between $(2, -3)$ and $(3, 0)$:
  $\Delta y = 0 - (-3) = 3$
  $\Delta x = 3 - 2 = 1$
  Slope $= \frac{3}{1} = 3$
• Between $(3, 0)$ and $(4, 3)$:
  $\Delta y = 3 - 0 = 3$
  $\Delta x = 4 - 3 = 1$
  Slope $= \frac{3}{1} = 3$

Since the slopes are all equal, the rate of change is the same between each pair of consecutive points.

Therefore, the rate of change is uniform.