Question
Identify which two lines are parallel.(1 point)Responsesy=12x+3 and y=12x−5y equals Start Fraction 1 over 2 End Fraction x plus 3 and y equals Start Fraction 1 over 2 End Fraction x minus 5y=13x+4 and y=13x+4y equals Start Fraction 1 over 3 End Fraction x plus 4 and y equals Start Fraction 1 over 3 End Fraction x plus 4y=23x−6 and y=−32x−6y equals two-thirds x minus 6 and y equals negative three-halves x minus 6y=−12x+6 and y=12x−8
Answers
GPT-4o mini
To identify which two lines are parallel, we need to compare the slopes of the given equations. Lines are parallel if they have the same slope.
1. **y = 12x + 3 and y = 12x - 5**
- Both have a slope of 12 (the coefficient of x).
2. **y = (1/2)x + 3 and y = (1/2)x - 5**
- Both have a slope of 1/2.
3. **y = 13x + 4 and y = 13x + 4**
- Both have a slope of 13.
4. **y = (1/3)x + 4 and y = (1/3)x + 4**
- Both have a slope of 1/3.
5. **y = 23x - 6 and y = -32x - 6**
- Different slopes: 23 and -32.
6. **y = (2/3)x - 6 and y = (-3/2)x - 6**
- Different slopes: 2/3 and -3/2.
7. **y = -12x + 6 and y = 12x - 8**
- Different slopes: -12 and 12.
The pairs of lines that are parallel are:
- **y = 12x + 3 and y = 12x - 5** (both have a slope of 12)
- **y = (1/2)x + 3 and y = (1/2)x - 5** (both have a slope of 1/2)
- **y = 13x + 4 and y = 13x + 4** (both have a slope of 13)
- **y = (1/3)x + 4 and y = (1/3)x + 4** (both have a slope of 1/3)
In summary, the first pair **(y = 12x + 3 and y = 12x - 5)** and the second pair **(y = (1/2)x + 3 and y = (1/2)x - 5)** are both examples of parallel lines.
1. **y = 12x + 3 and y = 12x - 5**
- Both have a slope of 12 (the coefficient of x).
2. **y = (1/2)x + 3 and y = (1/2)x - 5**
- Both have a slope of 1/2.
3. **y = 13x + 4 and y = 13x + 4**
- Both have a slope of 13.
4. **y = (1/3)x + 4 and y = (1/3)x + 4**
- Both have a slope of 1/3.
5. **y = 23x - 6 and y = -32x - 6**
- Different slopes: 23 and -32.
6. **y = (2/3)x - 6 and y = (-3/2)x - 6**
- Different slopes: 2/3 and -3/2.
7. **y = -12x + 6 and y = 12x - 8**
- Different slopes: -12 and 12.
The pairs of lines that are parallel are:
- **y = 12x + 3 and y = 12x - 5** (both have a slope of 12)
- **y = (1/2)x + 3 and y = (1/2)x - 5** (both have a slope of 1/2)
- **y = 13x + 4 and y = 13x + 4** (both have a slope of 13)
- **y = (1/3)x + 4 and y = (1/3)x + 4** (both have a slope of 1/3)
In summary, the first pair **(y = 12x + 3 and y = 12x - 5)** and the second pair **(y = (1/2)x + 3 and y = (1/2)x - 5)** are both examples of parallel lines.