Answer
$\text{(a)} \quad m=2$, $b=3$.
$\text{(b)} \quad $Refer to the graph below.
$\text{(c)} \quad2$.
$\text{(d)} \quad$increasing.
Work Step by Step
Given: $\quad f(x)=2x+3$
$\text{(a)}$ Compare with right side of the given function with the right side of the slope-intercept form $y=mx+b$. We can determine the slope as $m=2$ and $y$-intercept as $b=3$.
$\text{(b)}$ Start at $(0,3)$. With a slope of $2$, move $1$ unit to the right then move $2$ units upward to reach $(1,5)$. Connect the two points using a straight line. Refer to the graph below.
$\text{(c)}$ The average rate of change $R$ is the slope of the line so in this case, thus $R=m=2$.
$\text{(d)}$ The slope is positive so the linear function is increasing.
