The equation given is:

$4y = 5x + 20$

To find the intercepts, we will calculate the $x$-intercept and $y$-intercept by solving for when $y = 0$ and $x = 0$ respectively.

Step 1: Find the $y$-intercept

The $y$-intercept is the point where $x = 0$.

Substitute $x = 0$ into the equation:

$4y = 5(0) + 20$ $4y = 20$ $y = \frac{20}{4} = 5$

So, the $y$-intercept is $(0, 5)$.

Step 2: Find the $x$-intercept

The $x$-intercept is the point where $y = 0$.

Substitute $y = 0$ into the equation:

$4(0) = 5x + 20$ $0 = 5x + 20$ $5x = -20$ $x = \frac{-20}{5} = -4$

So, the $x$-intercept is $(-4, 0)$.

Step 3: Plot and graph

Now, you can plot the points $(0, 5)$ and $(-4, 0)$ on the graph and then draw a straight line through those points to complete the graph.

Would you like further details or have any questions? Here are some related questions:

1. How do you find intercepts for other linear equations?
2. What happens when there are no $x$- or $y$-intercepts?
3. How can slope-intercept form help with graphing lines?
4. How does the slope of the line relate to the intercepts?
5. Can you rewrite the given equation in slope-intercept form?

Tip: Remember, the slope is the change in $y$ over the change in $x$ between any two points on the line.