Question

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

3x−4y=8
3 x minus 4 y equals 8

4x−3y=12
4 x minus 3 y equals 12

3x−4y=12
3 x minus 4 y equals 12

4x−3y=6

Answer 1

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

The equation \( y = \frac{3}{4}x - 2 \) is already in slope-intercept form \( y = mx + b \), where \( m \) is the slope. Here, the slope \( m = \frac{3}{4} \).

For two lines to be parallel, they must have the same slope. We can convert the other equations into slope-intercept form and compare their slopes.

1. **Equation: \( 3x - 4y = 8 \)**
- Rearranging gives:
\[
-4y = -3x + 8 \\
y = \frac{3}{4}x - 2
\]
**Slope is \( \frac{3}{4} \)** (parallel).

2. **Equation: \( 4x - 3y = 12 \)**
- Rearranging gives:
\[
-3y = -4x + 12 \\
y = \frac{4}{3}x - 4
\]
**Slope is \( \frac{4}{3} \)** (not parallel).

3. **Equation: \( 3x - 4y = 12 \)**
- Rearranging gives:
\[
-4y = -3x + 12 \\
y = \frac{3}{4}x - 3
\]
**Slope is \( \frac{3}{4} \)** (parallel).

4. **Equation: \( 4x - 3y = 6 \)**
- Rearranging gives:
\[
-3y = -4x + 6 \\
y = \frac{4}{3}x - 2
\]
**Slope is \( \frac{4}{3} \)** (not parallel).

Based on this analysis, the lines that are parallel to \( y = \frac{3}{4}x - 2 \) are:
- **\( 3x - 4y = 8 \)**
- **\( 3x - 4y = 12 \)**

So, the final answer includes both equations **\( 3x - 4y = 8 \)** and **\( 3x - 4y = 12 \)**.