Answer
$\text{(a)}$ $m=-1$, $b=6$
$\text{(b)}$ See graph below.
$\text{(c)}$ $-1$
$\text{(d)}$ decreasing
Work Step by Step
Given $p(x)=-x+6$, we have:
$\text{(a)}$ Compare with the slope-intercept form $y=mx+b$, we can determine the slope as $m=-1$ and $y$-intercept as $b=6$.
$\text{(b}$ Start from $(0,6)$. With a slope of $-1$, move $1$ unit right, then $1$ unit down to reach $(1,5)$. Connect the two points using a straigh line to complete the graph. Refer to the graph below.
$\text{(c)}$ The average rate of change $R$ is the slope in this case, thus $R=m=-1$.
$\text{(d)}$ We can see from the graph that the linear function is decreasing, consistent with having a negative slope.
