#### Answer

(a) Slope $= 5$ and y-intercept $=-4$
(b) See the image.
(c) Average rate of change $= 5.0$
(d) The linear function $g(x)=5x-4$ is increasing.

#### Work Step by Step

Step-1: Compare the given equation with the point-slope form of the linear equation, that is, $g(x) = mx+b$, where $m$ is the slope of the linear function and $b$ is its y-intercept. By comparing $$g(x)=5x-4$$ to $$g(x) = mx+b$$ we understand that the slope of the given function is $5$ and its y-intercept is $-4$.
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 $x=-2$, $g(x)=-14$
For $x=-1$, $g(x)=-9$
For $x=0$, $g(x)=-4$
For $x=1$, $g(x)=1$
For $x=2$, $g(x) = 6$
This data obtains the graph shown.
Step-3: The average rate of change is defined as follows:
$$\frac{\Delta y}{\Delta x}=\frac{g(x_2)-g(x_1)}{x_2-x_1}$$
Let us calculate the average rate of change between $x_2=2$ and $x_1=-2$,
$$\frac{\Delta y}{\Delta x}=\frac{6-(-14)}{2-(-2)}=5$$
Step-4: Since slope, $m=5>0$, this linear function is increasing.