Answer
$\text{(a)}$ $m=-3$, $b=4$.
$\text{(b)}$ See graph.
$\text{(c)}$ $-3$.
$\text{(d)}$ decreasing.
Work Step by Step
Given $h(x)=-3x+4$, we have:
$\text{(a)}$ Comparing with the slope-intercept form $y=mx+b$, we can determine the slope as $m=-3$ and $y$-intercept as $b=4$.
$\text{(b)}$ The slope is $-3$ so start from $(0,4)$ then move $1$ unit to the right, then $3$ units down to reach $(1,1)$. Complete the graph by connecting the two points. See graph below.
$\text{(c)}$ The average rate of change $R$ is the slope in this case, thus $R=m=-3$.
$\text{(d)}$ We can see from the graph that the linear function is decreasing. This is consistent with the slope being negative.
