Answer
(a). $1$,
(b). $y=x+3$
Work Step by Step
(a). From $x_1=-1$ to $x_2=2$, we have the average rate of change as $\frac{g(x_2)-g(x_1)}{x_2-x_1}=\frac{((2)^2+1)-((-1)^2+1)}{2+1}=1$,
(b). The slope of the secant line is the same as the average rate of change in (a), $m=1$, use one point $(-1,2))$, we can find the equation as $y-2=(x+1)$ or $y=x+3$
