Analyzing Rate of Change: X-Y Table Analysis from 2 to 8

To solve this problem, we'll follow these steps:

• Step 1: Calculate the rate of change between each pair of consecutive points.
• Step 2: Compare the computed rates to determine if they are equal.
• Step 3: Conclude whether the rate of change is uniform or not.

Now, let's work through each step:
Step 1: Calculate the rate of change between each pair of consecutive points:
- Between $(2, 3)$ and $(4, 6)$:
$\text{Slope} = \frac{6 - 3}{4 - 2} = \frac{3}{2} = 1.5$
- Between $(4, 6)$ and $(6, 9)$:
$\text{Slope} = \frac{9 - 6}{6 - 4} = \frac{3}{2} = 1.5$
- Between $(6, 9)$ and $(8, 12)$:
$\text{Slope} = \frac{12 - 9}{8 - 6} = \frac{3}{2} = 1.5$

Step 2: Compare the computed rates:
- In all cases, the rate of change is $1.5$.

Step 3: Conclude that the rate of change is uniform across the expressed intervals.

Therefore, the rate of change for the given points is uniform.