To graph the equation \( 2x + 3y = -6 \), we need to rearrange it into slope-intercept form (\( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.

### Step 1: Solve for \( y \)

Starting with the equation:

\[
2x + 3y = -6
\]

Subtract \( 2x \) from both sides:

\[
3y = -2x - 6
\]

Now, divide by 3:

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

### Step 2: Identify the slope and y-intercept

From the equation \( y = -\frac{2}{3}x - 2 \), we can see that:

- The **slope** (\( m \)) is \( -\frac{2}{3} \).
- The **y-intercept** (\( b \)) is \( -2 \).

### Step 3: Plot the graph

1. Start by plotting the y-intercept \( (0, -2) \) on the graph (this is where the line crosses the y-axis).
2. From \( (0, -2) \), use the slope \( -\frac{2}{3} \). This means for every 3 units you move to the right (positive \( x \)-direction), move 2 units down (negative \( y \)-direction). Plot another point at \( (3, -4) \).
3. Draw a line passing through these points, and extend it in both directions.

This is the graph of the equation.

Would you like further explanation or help with another question? 

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Here are 5 related questions for further exploration:
1. How would the graph change if the equation was \( 2x + 3y = 6 \)?
2. What happens to the graph if the equation has a positive slope, like \( 2x - 3y = 6 \)?
3. How do you find the x-intercept of the equation?
4. What does the slope of \( -\frac{2}{3} \) represent in real-world terms?
5. Can you graph \( y = 2x - 1 \) and compare it with this equation?

**Tip**: Always convert the equation into slope-intercept form (\( y = mx + b \)) to make graphing easier!

Learn how to graph the linear equation 2x + 3y = -6. This step-by-step guide shows how to convert the equation into slope-intercept form, identify the slope and y-intercept, and plot the graph. Suitable for students in Grades 7-9.

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