We are tasked with finding the x-intercept and y-intercept of the line described by the equation:

$3x - 2y = -12$

1. Finding the x-intercept:

The x-intercept occurs when $y = 0$. Let's substitute $y = 0$ into the equation:

$3x - 2(0) = -12$ $3x = -12$ $x = \frac{-12}{3} = -4$

So, the x-intercept is $x = -4$.

2. Finding the y-intercept:

The y-intercept occurs when $x = 0$. Let's substitute $x = 0$ into the equation:

$3(0) - 2y = -12$ $-2y = -12$ $y = \frac{-12}{-2} = 6$

So, the y-intercept is $y = 6$.

Final Answer:

• x-intercept: $x = -4$
• y-intercept: $y = 6$

Would you like more details or further clarification?

Here are 5 related questions to extend this topic:

1. How do you find intercepts from a line in slope-intercept form?
2. Can a line have both x-intercepts and y-intercepts at the same point?
3. What do intercepts represent in real-world problems?
4. How can you graph a line using only the intercepts?
5. How do intercepts change if we modify the equation slightly?

Tip: When finding intercepts, always substitute the other variable as zero!