Answer
$\text{(a)}$ $m=-\frac{2}{3}$, $b=4$ ($y$-intercept).
$\text{(b)}$ See graph below.
$\text{(c)}$ $-\frac{2}{3}$.
$\text{(d)}$ decreasing
Work Step by Step
Given $h(x)=-\frac{2}{3}x+4$, we have:
$\text{(a)}$ Compare with the slope-intercept form $y=mx+b$, we can determine the slope as $m=-\frac{2}{3}$ and $y$-intercept as $b=4$.
$\text{(b)}$ Start from $(0,4)$. WIth a slope of $-\frac{2}{3}$, move $3$ units to the right, then $2$ units down to reach $(3,2)$. Complete the graph by connecting the two points using a straight line. Refer to the graph below.
$\text{(c)}$ The average rate of change $R$ is the slope in this case, thus $R=m=-\frac{2}{3}$.
$\text{(d)}$We can see from the graph that the linear function is decreasing, consistent with the fact that the slope is negative.
