To solve the equation \( 2x - 3y = 8 \) for \( y \), follow these steps:

1. **Isolate the term involving \( y \)** by subtracting \( 2x \) from both sides:
   \[
   -3y = 8 - 2x
   \]

2. **Divide both sides by \( -3 \)** to solve for \( y \):
   \[
   y = \frac{8 - 2x}{-3}
   \]

3. **Simplify the expression** (if needed):
   \[
   y = \frac{-8 + 2x}{3}
   \]
   or
   \[
   y = \frac{2x - 8}{3}
   \]

So, the solution for \( y \) is:
\[
y = \frac{2x - 8}{3}
\]

Would you like more details on any part of this process, or do you have any other questions?

Here are 5 related questions to expand your understanding:
1. How would the solution change if the equation were \( 2x + 3y = 8 \)?
2. Can you express \( x \) in terms of \( y \) from the original equation?
3. What happens to the equation if you substitute a specific value for \( x \)?
4. How would you graph the equation \( 2x - 3y = 8 \)?
5. What is the slope of the line represented by the equation \( 2x - 3y = 8 \)?

**Tip:** When solving for a variable, it's important to perform the inverse operations in the correct order to isolate the variable effectively.

Learn how to solve the linear equation 2x - 3y = 8 for y with a step-by-step solution. This problem covers key algebraic concepts, including linear equations and isolating variables. Suitable for students in Grades 7-9.

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