We are given the following information:

• Point A is at $(0, 0)$.
• Point B is the x-intercept of the line $6x - 4y = -12$.
• Point C is the y-intercept of the same line.

Step 1: Find Point B (the x-intercept)

To find the x-intercept, set $y = 0$ in the equation of the line $6x - 4y = -12$:

$6x - 4(0) = -12$ $6x = -12$ $x = -2$

So, Point B is $(-2, 0)$.

Step 2: Find Point C (the y-intercept)

To find the y-intercept, set $x = 0$ in the same equation:

$6(0) - 4y = -12$ $-4y = -12$ $y = 3$

So, Point C is $(0, 3)$.

Final Answer:

• Point B is $(-2, 0)$.
• Point C is $(0, 3)$.

Would you like a detailed sketch or further clarifications?

Here are five related questions for practice:

1. What would the equation of the line look like if the intercepts were different?
2. How would you calculate the midpoint between points B and C?
3. What is the slope of the line through points B and C?
4. How do the coordinates change if the line equation is modified to $2x - 3y = 6$?
5. Can you find the area of triangle ABC using these points?

Tip: To find intercepts, always set the other variable to zero in the line equation.