Answer
(a) $4$
(b) $y=4x-8$
Work Step by Step
(a) Given $h(x)=x^2-2x$, the average rate of change $R$ is given by the formula $$R=\dfrac{h(x_2)-h(x_1)}{x_2-x_1}$$
From $x_1=2$ to $x_2=4$, we have:
$$R=\dfrac{h(4)-h(2)}{4-2}=\dfrac{(4)^2-2(4)-((2)^2-2(2))}{2}=4$$
(b) The slope of the secant line is the average rate of change $m=4$.
To find the equation of the line, we need to use the coordinates of one point on the line. Since $(2, h(2))$ is on the line, find $h(2)$:
$h(2)=(2)^2-2(2)=0$
Thus, the line contains the point $(2, 0)$.
Therefore, using the point-slope form, the equation of the line is:
$$\begin{align*}
y-0&=4(x-2)\\
y&=4x-8
\end{align*}$$
