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Let's go through the problem step-by-step:

We are given the equation:

\[
2x - 3y = 9
\]

The goal is to solve for \( y \) by isolating it on one side of the equation. The instructions ask to fill in the blanks for the steps provided.

### Step 1: Subtract ____ from both sides of the equal.
To isolate \( y \), we first need to get rid of the term involving \( x \). So, we subtract \( 2x \) from both sides:

\[
2x - 3y - 2x = 9 - 2x
\]

This simplifies to:

\[
-3y = -2x + 9
\]

### Step 2: Divide both sides by ____.
Now, to fully isolate \( y \), divide both sides by \( -3 \) (since \( y \) is multiplied by \( -3 \)):

\[
y = \frac{-2x + 9}{-3}
\]

Simplifying the right-hand side:

\[
y = \frac{-2x}{-3} + \frac{9}{-3}
\]

\[
y = \frac{2x}{3} - 3
\]

Thus, the solution for \( y \) is:

\[
y = \frac{2x}{3} - 3
\]

### Answer:
- Step 1: Subtract **\( 2x \)** from both sides.
- Step 2: Divide both sides by **\( -3 \)**.

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. What does it mean to isolate a variable in an equation?
2. How do you know which term to subtract in step 1?
3. What are the rules for dividing both sides of an equation by a negative number?
4. How do you graph the equation \( y = \frac{2x}{3} - 3 \)?
5. What happens if you don’t subtract the right term in the first step?

**Tip**: Always remember to flip the sign when dividing by a negative number to keep the equation consistent.

In the following linear equation, solve for y. The goal is to get y on one side of the equal sign by following the steps: 2x - 3y = 9

This guide explains how to solve the linear equation 2x - 3y = 9 by isolating y. It covers basic algebraic operations and steps, suitable for students in Grades 6-8.

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