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To find the x-intercept and y-intercept of the line given by the equation \(2x - 3y = 6\), we need to follow these steps:

### Finding the x-intercept
The x-intercept is the point where the line crosses the x-axis. At this point, the value of \( y \) is 0.

1. Set \( y = 0 \) in the equation:
   \[
   2x - 3(0) = 6
   \]
2. Simplify the equation:
   \[
   2x = 6
   \]
3. Solve for \( x \):
   \[
   x = \frac{6}{2} = 3
   \]
So, the x-intercept is \( (3, 0) \).

### Finding the y-intercept
The y-intercept is the point where the line crosses the y-axis. At this point, the value of \( x \) is 0.

1. Set \( x = 0 \) in the equation:
   \[
   2(0) - 3y = 6
   \]
2. Simplify the equation:
   \[
   -3y = 6
   \]
3. Solve for \( y \):
   \[
   y = \frac{6}{-3} = -2
   \]
So, the y-intercept is \( (0, -2) \).

Therefore, the x-intercept and y-intercept of the line \( 2x - 3y = 6 \) are \( (3, 0) \) and \( (0, -2) \), respectively.

Would you like more details or have any questions about this solution? Here are five related questions you might find interesting:

1. How do you find the slope of the line given by the equation \(2x - 3y = 6\)?
2. What is the general form of a linear equation, and how does it relate to the slope-intercept form?
3. How can you graph the line \(2x - 3y = 6\) using the intercepts found?
4. How do you find the distance between two points on a graph?
5. What are parallel and perpendicular lines, and how can you determine if two lines are parallel or perpendicular?

**Tip:** Remember, intercepts provide quick and valuable points for graphing linear equations, helping to visualize and understand the line's behavior.

Find the x-intercept and the y-intercept of the line 2x - 3y = 6.

Learn how to find the x-intercept and y-intercept of the linear equation 2x - 3y = 6. This step-by-step guide covers key concepts such as setting y = 0 to find the x-intercept and x = 0 to find the y-intercept, suitable for students in Grades 8-10.

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