which is the rate of change for the interval between -6 and -3 on the x - axis?

Explanation:

Step1: Identify the formula for rate of change

The rate - of - change (slope) formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$.

Step2: Determine the points on the graph

When $x_1=-6$, $y_1 = 6$ and when $x_2=-3$, $y_2 = 2$.

Step3: Calculate the rate of change

$m=\frac{2 - 6}{-3-(-6)}=\frac{-4}{3}=-\frac{4}{3}$.

Answer:

$-\frac{4}{3}$