Question

Identify which two lines are parallel.

y = -1/2x + 6 and y = 1/2 x - 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 = 1/3 x + 4

Answer 1

To determine which lines are parallel, we need to identify lines that have the same slope. Let's examine the slopes of the given equations:

1. **y = -1/2x + 6**
- Slope = -1/2

2. **y = 1/2x - 8**
- Slope = 1/2

3. **y = 2/3x - 6**
- Slope = 2/3

4. **y = -3/2x - 6**
- Slope = -3/2

5. **y = 1/2x + 3**
- Slope = 1/2

6. **y = 1/2x - 5**
- Slope = 1/2

7. **y = 1/3x + 4**
- Slope = 1/3

8. **y = 1/3x + 4**
- Slope = 1/3

Now, let's identify groups of equations that have the same slopes:

- The lines **y = 1/2x - 8** and **y = 1/2x + 3** have the same slope of 1/2.
- The lines **y = 1/3x + 4** and **y = 1/3x + 4** (which are actually the same line) both have the same slope of 1/3.

Thus, the two lines that are parallel are:
**y = 1/2x - 8** and **y = 1/2x + 3**.