Answer
$\text{(a)}$ $m=5$, $b=-4$.
$\text{(b)}$ See graph below.
$\text{(c)}$ $5$
$\text{(d)}$ increasing.
Work Step by Step
Given $g(x)=5x-4$, we have:
$\text{(a)}$ Comparing with the slope-intercept form $y=mx+b$, we can determine the slope as $m=5$ and $y$-intercept as $b=-4$.
$\text{(b)}$ Start at $(0,-4)$. With a slope of $5$, move $1$ unit to the right , then $5$ units up to reach the point $(1,1)$. Connect the two points to complete the graph. Refer to the graph below.
$\text{(c)}$ The average rate of change $R$ is the slope in this case, thus $R=m=5$.
$\text{(d)}$ The graph rises from left to right (slope is poitive) therefore thelinear function is increasing.
