To find the rate of change, we need to calculate the difference in the [tex]\(y\)[/tex] values and the difference in the [tex]\(x\)[/tex] values between two points, and then divide these differences. Here's the step-by-step solution:
1. Choose two points from the given data:
We can select the first two points from the table:
[tex]\[
(-2, 17) \quad \text{and} \quad (-1, 13)
\][/tex]
2. Calculate the difference in [tex]\(x\)[/tex] values (Δx):
[tex]\[
Δx = x_2 - x_1 = -1 - (-2) = -1 + 2 = 1
\][/tex]
3. Calculate the difference in [tex]\(y\)[/tex] values (Δy):
[tex]\[
Δy = y_2 - y_1 = 13 - 17 = -4
\][/tex]
4. Calculate the rate of change:
[tex]\[
\text{Rate of change} = \frac{Δy}{Δx} = \frac{-4}{1} = -4
\][/tex]
Therefore, the rate of change is [tex]\(-4\)[/tex].
