Analyzing Rate of Change: Uniform Pattern in X-Y Coordinate Table

Question

Given a table showing points on the graph of a function, determine whether or not the rate of change is uniform.

00:00 Determine if the rate of change is uniform?

00:06 It appears that the change in X values is always equal

00:13 It appears that the change in Y values is always equal

00:17 Therefore the rate of change is uniform

00:20 And this is the solution to the question

To determine if the rate of change is uniform, we will follow these steps:

Let's work through the calculations:

Step 1: Calculate the rates of change (slopes) between consecutive points.

From $(-2, 6)$ to $(0, 8)$ : $\frac{8 - 6}{0 - (-2)} = \frac{2}{2} = 1.$

From $(0, 8)$ to $(2, 10)$ : $\frac{10 - 8}{2 - 0} = \frac{2}{2} = 1.$

From $(2, 10)$ to $(4, 12)$ : $\frac{12 - 10}{4 - 2} = \frac{2}{2} = 1.$

Step 2: Compare the rates.

All calculated rates are equal to 1, indicating that the rate of change is uniform.

Therefore, the solution to the problem is the rate of change is Uniform.

Uniform