The equation you provided is a linear equation in two variables, \( x \) and \( y \). You can approach solving or analyzing this equation in several ways, such as:

### 1. **Rearrange into Slope-Intercept Form:**
To write the equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept:
\[
3x - 2y = 6
\]
Solve for \( y \):
\[
-2y = -3x + 6
\]
\[
y = \frac{3}{2}x - 3
\]
Now, the equation is in the form \( y = \frac{3}{2}x - 3 \), where the slope \( m = \frac{3}{2} \) and the y-intercept is \( -3 \).

### 2. **Find the Intercepts:**
- To find the **x-intercept**, set \( y = 0 \) and solve for \( x \):
\[
3x - 2(0) = 6 \quad \Rightarrow \quad 3x = 6 \quad \Rightarrow \quad x = 2
\]
So the x-intercept is \( (2, 0) \).

- To find the **y-intercept**, set \( x = 0 \) and solve for \( y \):
\[
3(0) - 2y = 6 \quad \Rightarrow \quad -2y = 6 \quad \Rightarrow \quad y = -3
\]
So the y-intercept is \( (0, -3) \).

Would you like a deeper explanation of one of these methods or a graphical representation of the equation?

### Related Questions:
1. How do you graph a line from an equation?
2. What is the meaning of slope and intercept in linear equations?
3. How do you convert any linear equation to slope-intercept form?
4. What are parallel and perpendicular lines, and how are they related to slopes?
5. Can you explain how to solve systems of linear equations?

### Tip:
To quickly find intercepts, set the opposite variable to zero and solve. This provides key points to help graph the line easily.

Discover how to solve the linear equation 3x - 2y = 6 by converting it into slope-intercept form and finding the x- and y-intercepts. This guide is perfect for students in Grades 8-10 who are learning about linear equations and graphing.

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