Question

Which equation of a line is parallel to the equation -4x + 3y = 12?(1 point)
Responses

y =43x + 6
y =43x + 6

y=−43x + 4
y=−43x + 4

y = 3x + 12
y = 3x + 12

y = 4x + 8

Answer 1

To find a line that is parallel to the given equation \(-4x + 3y = 12\), we first need to determine the slope of that line. We can rewrite the equation in slope-intercept form (y = mx + b).

1. Start with the original equation:
\[
-4x + 3y = 12
\]

2. Solve for y:
\[
3y = 4x + 12
\]
\[
y = \frac{4}{3}x + 4
\]

The slope \(m\) of the line is \(\frac{4}{3}\).

Since parallel lines have the same slope, the equation of a line parallel to the given line will also have a slope of \(\frac{4}{3}\).

Now, let's look at the options provided:
- \(y = \frac{4}{3}x + 6\) (this has the correct slope)
- \(y = -\frac{4}{3}x + 4\) (this has a negative slope, not parallel)
- \(y = 3x + 12\) (this slope is 3, not parallel)
- \(y = 4x + 8\) (this slope is 4, not parallel)

The only equation that is parallel to the original line is:
\[
\text{y = } \frac{4}{3}x + 6
\]