Question
Identify which two lines are parallel.(1 point)
Responses
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+6 and y=12x−8
y equals negative Start Fraction 1 over 2 End Fraction x plus 6 and y equals Start Fraction 1 over 2 End Fraction x minus 8
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=23x−6 and y=−32x−6
y equals two-thirds x minus 6 and y equals negative three-halves x minus 6
Responses
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+6 and y=12x−8
y equals negative Start Fraction 1 over 2 End Fraction x plus 6 and y equals Start Fraction 1 over 2 End Fraction x minus 8
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=23x−6 and y=−32x−6
y equals two-thirds x minus 6 and y equals negative three-halves x minus 6
Answers
GPT-4o mini
To determine which two lines are parallel, we need to look for lines with the same slope.
1. **y = 13x + 4 and y = 13x + 4**
- Slope: 13 (both have the same slope, so they are parallel)
2. **y = 1/3 x + 4 and y = 1/3 x + 4**
- Slope: 1/3 (both have the same slope, so they are parallel)
3. **y = -12x + 6 and y = 12x - 8**
- Slopes: -12 and 12 (not parallel)
4. **y = -1/2 x + 6 and y = 1/2 x - 8**
- Slopes: -1/2 and 1/2 (not parallel)
5. **y = 12x + 3 and y = 12x - 5**
- Slope: 12 (both have the same slope, so they are parallel)
6. **y = 2/3 x - 6 and y = -3/2 x - 6**
- Slopes: 2/3 and -3/2 (not parallel)
From this analysis:
- The lines **y = 13x + 4 and y = 13x + 4** are parallel.
- The lines **y = 1/3 x + 4 and y = 1/3 x + 4** are also parallel.
- The lines **y = 12x + 3 and y = 12x - 5** are parallel as well.
Therefore, the pair of lines that is parallel from these options is **y = 12x + 3 and y = 12x - 5**. However, they are all technically instances of parallel lines in different contexts.
1. **y = 13x + 4 and y = 13x + 4**
- Slope: 13 (both have the same slope, so they are parallel)
2. **y = 1/3 x + 4 and y = 1/3 x + 4**
- Slope: 1/3 (both have the same slope, so they are parallel)
3. **y = -12x + 6 and y = 12x - 8**
- Slopes: -12 and 12 (not parallel)
4. **y = -1/2 x + 6 and y = 1/2 x - 8**
- Slopes: -1/2 and 1/2 (not parallel)
5. **y = 12x + 3 and y = 12x - 5**
- Slope: 12 (both have the same slope, so they are parallel)
6. **y = 2/3 x - 6 and y = -3/2 x - 6**
- Slopes: 2/3 and -3/2 (not parallel)
From this analysis:
- The lines **y = 13x + 4 and y = 13x + 4** are parallel.
- The lines **y = 1/3 x + 4 and y = 1/3 x + 4** are also parallel.
- The lines **y = 12x + 3 and y = 12x - 5** are parallel as well.
Therefore, the pair of lines that is parallel from these options is **y = 12x + 3 and y = 12x - 5**. However, they are all technically instances of parallel lines in different contexts.