https://file.aiquickdraw.com/mathbot/file/1726514575309jbgho7ti.jpg

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.

Point A is one vertex of triangle ABC. Point B is the x-intercept of 6x - 4y = -12 and point C is the y-intercept. What are points B and C? Sketch the triangle in the coordinate plane.

Learn how to find the x-intercept and y-intercept of the line 6x - 4y = -12. This problem covers key algebraic concepts like linear equations and coordinate geometry, including a step-by-step solution and sketch of the triangle formed by the intercepts. Suitable for students in Grades 8-10.

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