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