To find the x-intercept and y-intercept for the equation $3x - 2y = 6$, we follow these steps:

1. Find the x-intercept:

The x-intercept occurs where the line crosses the x-axis. At this point, the value of $y$ is 0. To find the x-intercept, set $y = 0$ and solve for $x$:

$3x - 2(0) = 6$ $3x = 6$ $x = \frac{6}{3} = 2$

So, the x-intercept is at $(2, 0)$.

2. Find the y-intercept:

The y-intercept occurs where the line crosses the y-axis. At this point, the value of $x$ is 0. To find the y-intercept, set $x = 0$ and solve for $y$:

$3(0) - 2y = 6$ $-2y = 6$ $y = \frac{6}{-2} = -3$

So, the y-intercept is at $(0, -3)$.

Summary:

• x-intercept: $(2, 0)$
• y-intercept: $(0, -3)$

Let me know if you'd like further explanation on any of the steps or have any questions!

Related Questions:

1. How do you graph the equation $3x - 2y = 6$?
2. How would you find the intercepts for a different linear equation?
3. What is the slope of the line represented by $3x - 2y = 6$?
4. How does the slope-intercept form of a linear equation compare to the standard form?
5. How do intercepts relate to the general equation of a line $Ax + By = C$?

Tip: When finding intercepts, always remember that the x-intercept occurs when $y = 0$ and the y-intercept occurs when (