Answer
$-3$
Work Step by Step
The general formula for average rate of change from $a$ to $b$ can be written as: $\dfrac{f(b)-f(a)}{b-a}$
Here, we have: $f(x)=4-3x$
Thus, we find the average rate of change as:
$\lim\limits_{x\to -2}\dfrac{f(x)-f(-2)}{x-(-2)}=\lim\limits_{x\to 2}\dfrac{(4-3x)-10}{x+2} \\=\lim\limits_{x\to -2}\dfrac{-3x-6}{x+2} \\=\lim\limits_{x\to -2}\dfrac{-3(x+2)}{x+2} \\=-3$
