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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.

Use the dot tool to plot the x- and y-intercepts, and then the line tool to graph a line based on those two points. The equation given is 4y = 5x + 20.

Learn how to graph the linear equation 4y = 5x + 20 by finding the x- and y-intercepts. This step-by-step guide demonstrates how to calculate intercepts and plot them on a graph to form the line. Suitable for students in Grades 8-10.

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