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.