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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

1 answer

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.