Answer
$-4$
Work Step by Step
Apply the rule such as: $\dfrac{f(b)-f(a)}{b-a}$ where $a \leq b$
Thus, the average rate is given as:
$\dfrac{f(b)-f(a)}{b-a}=\dfrac{f(a+h)-f(a)}{(a+h)-a}$
From, the given problem we have
$\dfrac{g(a+h)-g(a)}{(a+h)-a}=\dfrac{-4a-4h+2+4a-2}{h}$
This gives:
$\dfrac{g(a+h)-g(a)}{(a+h)-a}=\dfrac{-4h}{h}=-4$
Now, we can also see from the slope of the line $-4x+2$ that is $m=-4$
