Question

Which of the following lines would be parallel to y=34x−2
?(1 point)
Responses

4x−3y=6
4 x minus 3 y equals 6

3x−4y=12
3 x minus 4 y equals 12

3x−4y=8
3 x minus 4 y equals 8

4x−3y=12

Answer 1

To determine which lines are parallel to the line given by the equation \( y = 34x - 2 \), we need to identify the slope of this line first. The equation is in slope-intercept form \( y = mx + b \), where \( m \) represents the slope.

For the equation \( y = 34x - 2 \), the slope \( m \) is \( 34 \).

Lines are parallel if they have the same slope. Therefore, we need to rewrite the other equations in slope-intercept form (if they are not already) to find their slopes.

1. **For the equation \( 4x - 3y = 6 \):**
\[
-3y = -4x + 6
\]
\[
y = \frac{4}{3}x - 2
\]
(Slope = \( \frac{4}{3} \))

2. **For the equation \( 3x - 4y = 12 \):**
\[
-4y = -3x + 12
\]
\[
y = \frac{3}{4}x - 3
\]
(Slope = \( \frac{3}{4} \))

3. **For the equation \( 3x - 4y = 8 \):**
\[
-4y = -3x + 8
\]
\[
y = \frac{3}{4}x - 2
\]
(Slope = \( \frac{3}{4} \))

4. **For the equation \( 4x - 3y = 12 \):**
\[
-3y = -4x + 12
\]
\[
y = \frac{4}{3}x - 4
\]
(Slope = \( \frac{4}{3} \))

Now, comparing the slopes:

- **Slope of \( 4x - 3y = 6 \)**: \( \frac{4}{3} \)
- **Slope of \( 3x - 4y = 12 \)**: \( \frac{3}{4} \)
- **Slope of \( 3x - 4y = 8 \)**: \( \frac{3}{4} \)
- **Slope of \( 4x - 3y = 12 \)**: \( \frac{4}{3} \)

The lines that are parallel to \( y = 34x - 2 \) are:
- \( 4x - 3y = 6 \)
- \( 4x - 3y = 12 \)

Therefore, the correct answers are:
- \( 4x - 3y = 6 \)
- \( 4x - 3y = 12 \)

If you have to choose only one response, I would select either of the two with the same slope as the only options parallel to the original line.