Answer
(a). $-1$,
(b). $y=-x$
Work Step by Step
(a). From $x_1=-2$ to $x_2=1$, we have the average rate of change as $\frac{g(x_2)-g(x_1)}{x_2-x_1}=\frac{((1)^2-2)-((-2)^2-2)}{1+2}=-1$,
(b). The slope of the secant line is the same as the average rate of change in (a), $m=-1$, use one point $(1,-1))$, we can find the equation as $y+1=-(x-1)$ or $y=-x$
