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Let's solve the given equation step by step to find the slope and y-intercept.

The equation provided is:

\[
4x - 5y = 20
\]

We need to rewrite this equation in slope-intercept form, which is:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept.

### Step 1: Solve for \(y\)
First, isolate \(y\) on one side of the equation.

\[
4x - 5y = 20
\]

Subtract \(4x\) from both sides:

\[
-5y = -4x + 20
\]

Now, divide both sides by \(-5\) to solve for \(y\):

\[
y = \frac{-4x + 20}{-5}
\]

Simplify the terms:

\[
y = \frac{-4}{-5}x + \frac{20}{-5}
\]

\[
y = \frac{4}{5}x - 4
\]

### Step 2: Identify the slope and y-intercept
Now the equation is in slope-intercept form \(y = mx + b\), where:
- The slope \(m = \frac{4}{5}\)
- The y-intercept \(b = -4\)

### Final Answer:
- The slope is \(\frac{4}{5}\)
- The y-intercept is \(-4\)

You can now input the slope as \(\frac{4}{5}\) in the answer box.

Let me know if you'd like further clarification!

---

Here are some related questions you could explore:
1. How do you graph a line given its slope and y-intercept?
2. What does a slope of \(\frac{4}{5}\) mean in terms of rise over run?
3. How do you find the x-intercept from the slope-intercept form of a line?
4. What happens to the slope when the line is vertical?
5. How do you convert a slope-intercept equation back into standard form?

**Tip:** When solving for the slope, remember that the coefficient of \(x\) in slope-intercept form represents the slope directly!

Find the slope and y-intercept of the line. Graph the line. The equation is 4x - 5y = 20.

Learn how to find the slope and y-intercept of the equation 4x - 5y = 20. This step-by-step solution explains how to convert the equation into slope-intercept form and graph the line. Suitable for students in Grades 8-10.

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