Question

Identify which two lines are parallel.(1 point) Responses
y=−12x+6 and y=12x−8 y
y=13x+4 and y=13x+4
y=12x+3 and y=12x−5
y=23x−6 and y=−32x−6

Answer 1

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

1. **y = -12x + 6** has a slope of -12.
2. **y = 12x - 8** has a slope of 12.

3. **y = 13x + 4** has a slope of 13.
4. **y = 13x + 4** (again) has a slope of 13. (This pair of lines is identical.)

5. **y = 12x + 3** has a slope of 12.
6. **y = 12x - 5** has a slope of 12.

7. **y = 23x - 6** has a slope of 23.
8. **y = -32x - 6** has a slope of -32.

The pairs of lines with the same slope are:
- **y = 13x + 4 and y = 13x + 4**
- **y = 12x + 3 and y = 12x - 5**

Thus, the lines that are parallel are:
- **y = 12x + 3 and y = 12x - 5**.

In conclusion, these two lines are parallel:
- **y = 12x + 3** and **y = 12x - 5**.