#### Answer

(a) Slope $= 2$ and y-intercept $=3$
(b) See the image.
(c) Average rate of change $= 2.0$
(d) The linear function $f(x)=2x+3$ is increasing.

#### Work Step by Step

Step-1: Compare the given equation with the point-slope 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
$$f(x)=2x+3$$ to $$f(x) = mx+b$$ we understand that the slope of the given function is $2$ and its y-intercept 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 $x=-2$, $f(x)=-1$
For $x=-1$, $f(x)=1$
For $x=0$, $f(x)=3$
For $x=1$, $f(x)=5$
For $x=2$, $f(x) = 7$
This data yields the graph shown.
Step-3: The average rate of change is defined as follows:
$$\frac{\Delta y}{\Delta x}=\frac{f(x_2)-f(x_1)}{x_2-x_1}$$
Let us calculate average rate of change between $x_2=2$ and $x_1=-2$,
$$\frac{\Delta y}{\Delta x}=\frac{7-(-1)}{2-(-2)}=2$$
Step-4: Since slope, $m=2>0$, this linear function is increasing.