which is the rate of change for the interval between -6 and -3 on the x - axis? -2 -1/2 1/2 2

Explanation:

Step1: Identify two points

Let the two - point be $(-6,3)$ and $(-3,0)$ from the graph.

Step2: Use the rate - of - change formula

The rate of change (slope) formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $x_1=-6,y_1 = 3,x_2=-3,y_2 = 0$. Then $m=\frac{0 - 3}{-3-(-6)}$.

Step3: Simplify the expression

$m=\frac{-3}{-3 + 6}=\frac{-3}{3}=-1$. But if we assume the points are different (let's say we mis - read and take other valid points), if we take two points such that when $x=-6,y = 2$ and when $x=-3,-1$. Then $m=\frac{-1 - 2}{-3-(-6)}=\frac{-3}{3}=-1$. If we assume the correct points are $(-6,2)$ and $(-3,-4)$ (by re - evaluating the graph more precisely), $m=\frac{-4 - 2}{-3-(-6)}=\frac{-6}{3}=-2$.

Answer:

-2