Question

Identify which two lines are parallel.
y = -1/2x + 6 and y = 1/2x - 8
y = 2/3x - 6 and y = - 3/2x - 6
y = 1/2x + 3 and y =1/2x - 5
y = 1/3x + 4 and y = 1/3x + 4

Answer 1

To identify which two lines are parallel, we need to look at the slopes of each pair of lines. Lines are parallel if they have the same slope.

1. For the first pair:
- \(y = -\frac{1}{2}x + 6\) has a slope of \(-\frac{1}{2}\).
- \(y = \frac{1}{2}x - 8\) has a slope of \(\frac{1}{2}\).
- **Not parallel.**

2. For the second pair:
- \(y = \frac{2}{3}x - 6\) has a slope of \(\frac{2}{3}\).
- \(y = -\frac{3}{2}x - 6\) has a slope of \(-\frac{3}{2}\).
- **Not parallel.**

3. For the third pair:
- \(y = \frac{1}{2}x + 3\) has a slope of \(\frac{1}{2}\).
- \(y = \frac{1}{2}x - 5\) has a slope of \(\frac{1}{2}\).
- **Parallel.**

4. For the fourth pair:
- \(y = \frac{1}{3}x + 4\) has a slope of \(\frac{1}{3}\).
- \(y = \frac{1}{3}x + 4\) has a slope of \(\frac{1}{3}\).
- **Parallel.**

The two pairs of lines that are parallel are:
- \(y = \frac{1}{2}x + 3\) and \(y = \frac{1}{2}x - 5\)
- \(y = \frac{1}{3}x + 4\) and \(y = \frac{1}{3}x + 4\)

So, the answer is the third pair and the fourth pair of lines are parallel.