Question

Which lines are parallel to y=3/4 x -2?
I have as possible answers are:
1. 3x-4y=8
2. 3x-4y=12.
3. 4x-3y=6
4. 4x+3y=8

Answer 1

Thank you.

Answer 2

To determine which lines are parallel to the line given by the equation \( y = \frac{3}{4}x - 2 \), we need to identify the slope of the line.

The slope-intercept form of a line is \( y = mx + b \), where \( m \) is the slope. From the given equation \( y = \frac{3}{4}x - 2 \), we can see that the slope \( m \) is \( \frac{3}{4} \).

For a line to be parallel, it must have the same slope. Therefore, we need to check the slopes of the lines represented by the equations given in the possible answers.

1. **For \( 3x - 4y = 8 \)**:
- Rearranging to the slope-intercept form:
\[
-4y = -3x + 8 \implies y = \frac{3}{4}x - 2
\]
- The slope is \( \frac{3}{4} \).

2. **For \( 3x - 4y = 12 \)**:
- Rearranging to the slope-intercept form:
\[
-4y = -3x + 12 \implies y = \frac{3}{4}x - 3
\]
- The slope is \( \frac{3}{4} \).

3. **For \( 4x - 3y = 6 \)**:
- Rearranging to the slope-intercept form:
\[
-3y = -4x + 6 \implies y = \frac{4}{3}x - 2
\]
- The slope is \( \frac{4}{3} \).

4. **For \( 4x + 3y = 8 \)**:
- Rearranging to the slope-intercept form:
\[
3y = -4x + 8 \implies y = -\frac{4}{3}x + \frac{8}{3}
\]
- The slope is \( -\frac{4}{3} \).

Now, we can summarize:

- The lines **1 and 2** have the same slope \( \frac{3}{4} \) as \( y = \frac{3}{4}x - 2 \), which means these lines are parallel.
- The lines **3 and 4** have different slopes (\( \frac{4}{3} \) and \( -\frac{4}{3} \)), so they are not parallel to the given line.

**Final Answer**: The lines that are parallel to \( y = \frac{3}{4}x - 2 \) are:
1. \( 3x - 4y = 8 \)
2. \( 3x - 4y = 12 \)

Answer 3

You're welcome! If you have any more questions or need further assistance, feel free to ask. Happy studying!