Question
Which of the following is parallel to the line y=2/3x+5 ?
y=-2/3x+5
y=3/2x-4
y=2/3x -7
y=-3/2x+5
y=-2/3x+5
y=3/2x-4
y=2/3x -7
y=-3/2x+5
Answers
GPT-4o mini
To determine which of the given lines is parallel to the line \( y = \frac{2}{3}x + 5 \), we need to identify lines that have the same slope.
The slope of the given line \( y = \frac{2}{3}x + 5 \) is \( \frac{2}{3} \).
Now, let's analyze the slopes of the provided lines:
1. **For \( y = -\frac{2}{3}x + 5 \)**: The slope is \( -\frac{2}{3} \) (not parallel).
2. **For \( y = \frac{3}{2}x - 4 \)**: The slope is \( \frac{3}{2} \) (not parallel).
3. **For \( y = \frac{2}{3}x - 7 \)**: The slope is \( \frac{2}{3} \) (parallel).
4. **For \( y = -\frac{3}{2}x + 5 \)**: The slope is \( -\frac{3}{2} \) (not parallel).
The only line that is parallel to \( y = \frac{2}{3}x + 5 \) is:
**\( y = \frac{2}{3}x - 7 \)**.
The slope of the given line \( y = \frac{2}{3}x + 5 \) is \( \frac{2}{3} \).
Now, let's analyze the slopes of the provided lines:
1. **For \( y = -\frac{2}{3}x + 5 \)**: The slope is \( -\frac{2}{3} \) (not parallel).
2. **For \( y = \frac{3}{2}x - 4 \)**: The slope is \( \frac{3}{2} \) (not parallel).
3. **For \( y = \frac{2}{3}x - 7 \)**: The slope is \( \frac{2}{3} \) (parallel).
4. **For \( y = -\frac{3}{2}x + 5 \)**: The slope is \( -\frac{3}{2} \) (not parallel).
The only line that is parallel to \( y = \frac{2}{3}x + 5 \) is:
**\( y = \frac{2}{3}x - 7 \)**.