To solve the equation \(5x - 4y - 20 = 0\), we can rewrite it in different forms or find specific solutions. Let's start by solving for \(y\) in terms of \(x\):

### Solving for \(y\):
1. Start with the given equation:
   \[
   5x - 4y - 20 = 0
   \]
   
2. Add 20 to both sides:
   \[
   5x - 4y = 20
   \]
   
3. Subtract \(5x\) from both sides:
   \[
   -4y = -5x + 20
   \]
   
4. Divide everything by \(-4\) to isolate \(y\):
   \[
   y = \frac{5x - 20}{4}
   \]
   Simplifying:
   \[
   y = \frac{5}{4}x - 5
   \]

So, the equation in slope-intercept form is:
\[
y = \frac{5}{4}x - 5
\]

This tells us that the slope of the line is \(\frac{5}{4}\), and the y-intercept is \(-5\).

Would you like more details on graphing this, or do you have any other questions?

Here are 5 related questions for further exploration:
1. How do we find the x-intercept of this line?
2. Can we solve this equation using substitution with a given value of \(x\) or \(y\)?
3. What is the slope of a line perpendicular to this one?
4. How do you graph this equation step by step?
5. What is the equation of a line parallel to this one passing through a specific point?

**Tip:** Always check if an equation can be simplified before solving, as it makes the process easier.

Learn how to solve the linear equation 5x - 4y - 20 = 0 by converting it into slope-intercept form. This step-by-step guide demonstrates key algebraic concepts like finding the slope and y-intercept, making it ideal for students in Grades 8-10.

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