https://file.aiquickdraw.com/mathbot/file/172627628119070fon0wi.jpg

The equation in the image is:

\[
4x - 5y - 20 = 0
\]

We need to solve for \( y \). Here’s the step-by-step solution:

1. Start with the given equation:
   \[
   4x - 5y - 20 = 0
   \]

2. Add 20 to both sides of the equation:
   \[
   4x - 5y = 20
   \]

3. Subtract \( 4x \) from both sides to isolate the \( y \)-term:
   \[
   -5y = -4x + 20
   \]

4. Finally, divide both sides by \(-5\) to solve for \( y \):
   \[
   y = \frac{-4x + 20}{-5}
   \]

5. Simplify the expression:
   \[
   y = \frac{4x}{5} - 4
   \]

So the solution for \( y \) is:

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

Would you like more details or have any questions?

---

Here are 5 related questions to consider:
1. How do you solve linear equations with two variables?
2. What is the importance of isolating the variable in an equation?
3. How does dividing by negative numbers affect the signs in an equation?
4. Can this equation be graphed? If so, how would the graph look?
5. How can this method be applied to more complex algebraic expressions?

**Tip:** Always double-check your operations, especially when dealing with negative signs during division.

This problem explains how to solve a linear equation 4x - 5y - 20 = 0 for y using algebraic techniques. Ideal for students in Grades 8-10, covering linear equation concepts and how to isolate variables.

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