Which graph represents this equation?

To determine which graph represents the equation \(-3x + 4y = -12\), we can rewrite it in slope-intercept form (y = mx + b) or find the intercepts.

1. **Find the y-intercept (when \(x = 0\))**:
\[
-3(0) + 4y = -12 \implies 4y = -12 \implies y = -3
\]
So the y-intercept is \((0, -3)\).

2. **Find the x-intercept (when \(y = 0\))**:
\[
-3x + 4(0) = -12 \implies -3x = -12 \implies x = 4
\]
So the x-intercept is \((4, 0)\).

Now we have two points: \((0, -3)\) and \((4, 0)\).

Next, we can analyze the options:

- **Option : Points \((-4, 0)\) and \((0, -3)\) - this does not match our intercepts.
- **Option B**: Points \((0, 3)\) and \((4, 0)\) - this does not match, as the y-intercept is \(-3\), not \(3\).
- **Option C**: Points \((0, -3)\) and \((4, 0)\) - this matches perfectly with our intercepts.
- **Option D**: Points \((-4, 0)\) and \((0, 3)\) - this does not match.

Based on the analysis, the correct answer is:

**C. A graph is a line that extends from third quadrant to first quadrant through left parenthesis 0, negative 3 right parenthesis, and left parenthesis 4, 0 right parenthesis.**