Question

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

3x−4y=12
3 x minus 4 y equals 12

4x−3y=12
4 x minus 3 y equals 12

3x−4y=8
3 x minus 4 y equals 8

4x−3y=6

Answer 1

To find a line that is parallel to \( y = 34x - 2 \), we need to look for lines that have the same slope. The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope.

In the equation \( y = 34x - 2 \), the slope (\( m \)) is \( 34 \). Therefore, we are looking for lines that also have a slope of \( 34 \).

Let's examine the equations provided:

1. **3x - 4y = 12**

Rearranging it into the slope-intercept form:
\[
-4y = -3x + 12 \\
y = \frac{3}{4}x - 3
\]
(Slope is \( \frac{3}{4} \))

2. **4x - 3y = 12**

Rearranging it into the slope-intercept form:
\[
-3y = -4x + 12 \\
y = \frac{4}{3}x - 4
\]
(Slope is \( \frac{4}{3} \))

3. **3x - 4y = 8**

Rearranging it into the slope-intercept form:
\[
-4y = -3x + 8 \\
y = \frac{3}{4}x - 2
\]
(Slope is \( \frac{3}{4} \))

4. **4x - 3y = 6**

Rearranging it into the slope-intercept form:
\[
-3y = -4x + 6 \\
y = \frac{4}{3}x - 2
\]
(Slope is \( \frac{4}{3} \))

None of the provided equations has a slope of \( 34 \). Therefore, none of the given choices are parallel to the line \( y = 34x - 2 \).

If the answer requires a line parallel to the original, each option fails to have the required slope \( 34\).