Answer
(a) -4
(b) the slope is also -4
Work Step by Step
(a) We find the average rate of change from $x=a$ to $x=a+h$:
$\frac{g(a+h)-g(a)}{(a+h)-a}=\frac{[-4(a+h)+2]-[-4a+2]}{h}=\frac{-4a-4h+2+4a-2}{h}=\frac{-4h}{h}=-4$
(b) A line has the form $f(x)=mx+b$, with $m=slope$.
For the line $g(x)=-4x+2$, the slope is $\displaystyle -4$, which equals what we got in (a).
