Question

Which equation of a line is parallel to the equation -4x + 3y = 12?
A. y = - 4/3 x + 6
B. y = 4x + 8
C. y = 4/3 x + 6
D. y = 3x + 12

Answer 1

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:

1. Start with the original equation: \(-4x + 3y = 12\).
2. Add \(4x\) to both sides: \(3y = 4x + 12\).
3. 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. \(y = \frac{4}{3}x + 6\)**.