Answer
$\text{(a)}$ $m=\frac{1}{4}$, $b=-3$
$\text{(b)}$ See graph below.
$\text{(c)}$ $\frac{1}{4}$
$\text{(a)}$ increasing
Work Step by Step
Given $f(x)=\frac{1}{4}x-3$, we have:
$\text{(a)}$ Compare with the slope-intercept form $y=mx+b$, we can determine the slope as $m=\frac{1}{4}$ and $y$-intercept as $b=-3$.
$\text{(b)}$ Start from $(0,-3)$. With a slope of $\frac{1}{4}$, move $4$ units right, then $1$ unit up to reach $(4,-2)$. Complete the graph by connecting the two points. Refer to the graph below.
$\text{(c)}$ The average rate of change $R$ is the slope in this case, thus $R=m=\frac{1}{4}$.
$\text{(d)}$ We can see from the graph that the linear function is increasing, consistent with having a positive slope.
