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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

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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.