#### Answer

a) Slope $=\frac{1}{4}$ and y-intercept $=−3$
(b) See the image.
(c) Average rate of change $=\frac{1}{4}=0.25$
(d) The linear function $f(x)=\frac{1}{4}x−3$ is increasing.

#### Work Step by Step

Step-1: Compare the given equation with the slope-intercept form of the linear equation, that is, $f(x)=mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing
$$f(x)=\frac{1}{4}x−3$$
to
$$f(x)=mx+b$$
we understand that the slope of the given function is −3.
Step-2: Let us put values of $x$ from $−2$ to $2$ into the function to obtain corresponding $y$ values. Using this we can plot a graph. Thus,
For $x=−2$,$ f(x)=−\frac{7}{2}=−3.5$
For $x=−1$, $f(x)=−\frac{13}{4}=−3.25$
For$ x=0$, $f(x)=−3$
For$ x=1$,$ f(x)=−\frac{11}{4}=−2.75$
For$ x=2$, $f(x)=−\frac{5}{2}=−2.5$
This data obtains the graph shown.
Step-3: The average rate of change is defined as follows:
$$\frac{Δy}{Δx}=\frac{f(x_2)−f(x_1)}{x_2−x_1}$$
Let us calculate the average rate of change between $x_2=2$ and
$x_1=−2$,
$$\frac{Δy}{Δx}=\frac{−2.5−(−3.5)}{2−(−2)}=\frac{1}{4}=0.25$$
Step-4: Since slope, $m=0.25>0$, this linear function is increasing.