How to use the intercepts to graph the equation x - 4 y = -...

Where the line crosses the y-axis is known as the y-intercept, and x = 0. The x-intercept is where the line crosses the x-axis and y = 0. This will give you two points on your line.
Determine the y-intercept, where x = 0.
${\displaystyle 0-4y=-8}$
${\displaystyle -4y=-8}$
Divide both sides by -4.
${\displaystyle y=2}$
Where y = 0, find the x-intercept.
${\displaystyle x-0y=-8}$
${\displaystyle x=-8}$
So now you have two points on your line with the y-intercept and x-intercept: (0, 2), representing ${\displaystyle (x_1,y_1)}$; and (-8, 0), representing ${\displaystyle (x_2,y_2)}$.
Now that you have two points on the line, you can determine the slope, m, using the equation ${\displaystyle m}$ = ${\displaystyle \frac{(y_2-y_1)}{(x_2-x_1)}}$.
For this line:
${\displaystyle m}$ = ${\displaystyle \frac{(0-2)}{(-8-0)}=-\frac{2}{-8}=\frac{1}{4}}$
The following is a graph of the line showing the y-intercept of 2 and the x-intercept of -8.