To graph the equation \( 3x - 2y - 6 = 0 \), let's rewrite it in slope-intercept form (i.e., \( y = mx + b \)), where \( m \) is the slope and \( b \) is the y-intercept.

### Steps:

1. Start with the equation:
   \[
   3x - 2y - 6 = 0
   \]

2. Solve for \( y \):
   \[
   -2y = -3x + 6
   \]
   \[
   y = \frac{3}{2}x - 3
   \]

Now, the equation is in the form \( y = \frac{3}{2}x - 3 \). The slope is \( \frac{3}{2} \) and the y-intercept is \( -3 \).

### Plotting the Graph:

- **Y-intercept**: The graph crosses the y-axis at \( (0, -3) \).
- **Slope**: The slope \( \frac{3}{2} \) means that for every 2 units you move horizontally (to the right), you move 3 units vertically (upwards).

You can plot the point \( (0, -3) \), and then use the slope to find another point. Starting from \( (0, -3) \), go 2 units to the right and 3 units up to reach the point \( (2, 0) \).

Now, draw a straight line through the points \( (0, -3) \) and \( (2, 0) \). That will be the graph of the equation.

Would you like me to generate the visual graph for you?

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**Related Questions:**

1. What is the importance of the slope in linear equations?
2. How can we find the x-intercept of this equation?
3. How does changing the slope affect the graph?
4. Can you graph a vertical line from a linear equation?
5. What is the general form of a linear equation?

**Tip**: Always double-check your calculations when converting an equation to slope-intercept form.

Learn how to graph the linear equation 3x - 2y - 6 = 0 by converting it into slope-intercept form. This tutorial explains the slope, y-intercept, and step-by-step process to plot the graph. Suitable for students in Grades 8-10.

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