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

Question

Responses

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

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

y = 4x + 8
y = 4x + 8

y=−43x + 4

Answer 1

To find an equation of a line that is parallel to the equation \(-4x + 3y = 12\), we first need to determine the slope of the given line.

1. Rewrite the equation in slope-intercept form (y = mx + b):

   \(-4x + 3y = 12\)

   Add \(4x\) to both sides:

   \(3y = 4x + 12\)

   Now, divide by 3:

   \(y = \frac{4}{3}x + 4\)

From this, we see that the slope (m) of the line is \(\frac{4}{3}\).

2. A line parallel to this one will have the same slope. Therefore, any equation of the form \(y = \frac{4}{3}x + b\) (where \(b\) can be any number) will be parallel to the given line.

Now, let’s evaluate the response options to see which one matches the parallel condition:

• y = 3x + 12 (Slope is 3, not \(\frac{4}{3}\))
• y = \frac{43}{3}x + 6 (Slope is \(\frac{43}{3}\), not \(\frac{4}{3}\))
• y = 4x + 8 (Slope is 4, not \(\frac{4}{3}\))
• y = -\frac{43}{3}x + 4 (Slope is \(-\frac{43}{3}\), not \(\frac{4}{3}\))

None of the options provided have a slope of \(\frac{4}{3}\), so none of them represent a line that is parallel to the original line.

Therefore, based on the options given, none is correct.