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!