To find a line that is parallel to the equation \(-4x + 3y = 12\), we need to first determine its slope.
We can write the given equation in slope-intercept form (y = mx + b) by solving for y:
- Start with the original equation: \(-4x + 3y = 12\).
- Add \(4x\) to both sides: \(3y = 4x + 12\).
- Divide each term by 3: \(y = \frac{4}{3}x + 4\).
From this, we see that the slope (m) of the original line is \(\frac{4}{3}\).
Since parallel lines have the same slope, any line that has a slope of \(\frac{4}{3}\) will be parallel to the original line.
Now let's check the slopes of the options provided:
A. \(y = -\frac{4}{3}x + 6\) (slope = -\(\frac{4}{3}\)) B. \(y = 4x + 8\) (slope = 4) C. \(y = \frac{4}{3}x + 6\) (slope = \(\frac{4}{3}\)) D. \(y = 3x + 12\) (slope = 3)
Looking through the options, we see that:
- Option C: \(y = \frac{4}{3}x + 6\) has the same slope as the original line.
Therefore, the correct answer is:
C. \(y = \frac{4}{3}x + 6\).