Which of the following lines would be parallel to y=3/4x−2 ?(1 point)

Question

Responses

4x−3y=6
4 x minus 3 y equals 6

3x−4y=12
3 x minus 4 y equals 12

4x−3y=12
4 x minus 3 y equals 12

3x−4y=8

Answer 1

To determine which of the given lines is parallel to \( y = \frac{3}{4}x - 2 \), we need to find lines with the same slope. The slope of the given line is \( \frac{3}{4} \).

Let's analyze the slopes of the lines given in standard form:

1. For the line \( 4x - 3y = 6 \):

   • Rearranging to slope-intercept form ( \( y = mx + b \)): \[ -3y = -4x + 6 \ y = \frac{4}{3}x - 2 \]
   • Slope: \( \frac{4}{3} \) (not parallel)

2. For the line \( 3x - 4y = 12 \):

   • Rearranging: \[ -4y = -3x + 12 \ y = \frac{3}{4}x - 3 \]
   • Slope: \( \frac{3}{4} \) (parallel)

3. For the line \( 4x - 3y = 12 \):

   • Rearranging: \[ -3y = -4x + 12 \ y = \frac{4}{3}x - 4 \]
   • Slope: \( \frac{4}{3} \) (not parallel)

4. For the line \( 3x - 4y = 8 \):

   • Rearranging: \[ -4y = -3x + 8 \ y = \frac{3}{4}x - 2 \]
   • Slope: \( \frac{3}{4} \) (parallel)

The lines \( 3x - 4y = 12 \) and \( 3x - 4y = 8 \) are both parallel to \( y = \frac{3}{4}x - 2 \).

Thus, the correct answers are \( 3x - 4y = 12 \) and \( 3x - 4y = 8 \).