To determine which two lines are parallel, we need to look for lines with the same slope.
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y = 13x + 4 and y = 13x + 4
- Slope: 13 (both have the same slope, so they are parallel)
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y = 1/3 x + 4 and y = 1/3 x + 4
- Slope: 1/3 (both have the same slope, so they are parallel)
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y = -12x + 6 and y = 12x - 8
- Slopes: -12 and 12 (not parallel)
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y = -1/2 x + 6 and y = 1/2 x - 8
- Slopes: -1/2 and 1/2 (not parallel)
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y = 12x + 3 and y = 12x - 5
- Slope: 12 (both have the same slope, so they are parallel)
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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.