Question

Identify which two lines are parallel.(1 point)
Responses

y=23x−6
and y=−32x−6
y equals two-thirds x minus 6 and y equals negative three-halves x minus 6

y=13x+4
and y=13x+4
y equals Start Fraction 1 over 3 End Fraction x plus 4 and y equals Start Fraction 1 over 3 End Fraction x plus 4

y=12x+3
and y=12x−5
y equals Start Fraction 1 over 2 End Fraction x plus 3 and y equals Start Fraction 1 over 2 End Fraction x minus 5

y=−12x+6
and y=12x−8

Answer 1

To identify which two lines are parallel, we need to look for equations that have the same slope.

1. **y = 23x - 6** and **y = -32x - 6**
- Slopes: 23 and -32 (not parallel)

2. **y = (2/3)x - 6** and **y = (-3/2)x - 6**
- Slopes: 2/3 and -3/2 (not parallel)

3. **y = 13x + 4** and **y = 13x + 4**
- Slopes: 13 and 13 (parallel)

4. **y = 12x + 3** and **y = 12x - 5**
- Slopes: 12 and 12 (parallel)

5. **y = -12x + 6** and **y = 12x - 8**
- Slopes: -12 and 12 (not parallel)

The pairs of parallel lines are **y = 13x + 4** and **y = 13x + 4**, and also **y = 12x + 3** and **y = 12x - 5**.

Since the question asks for which two lines are parallel, you can choose either pair. But strictly speaking, the best answer based purely on their equality is:
- **y = 13x + 4** and **y = 13x + 4** (they are the exact same line).