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Identify which two lines are parallel.

y = -1/2x + 6 and y = 1/2 x - 8
y = 2/3x - 6 and y = -3/2x - 6
y= 1/2x + 3 and y = 1/2x - 5
y= 1/3x + 4 and y = 1/3 x + 4

1 answer

To determine which lines are parallel, we need to identify lines that have the same slope. Let's examine the slopes of the given equations:

  1. y = -1/2x + 6

    • Slope = -1/2

  2. y = 1/2x - 8

    • Slope = 1/2

  3. y = 2/3x - 6

    • Slope = 2/3

  4. y = -3/2x - 6

    • Slope = -3/2

  5. y = 1/2x + 3

    • Slope = 1/2

  6. y = 1/2x - 5

    • Slope = 1/2

  7. y = 1/3x + 4

    • Slope = 1/3

  8. y = 1/3x + 4

    • Slope = 1/3

Now, let's identify groups of equations that have the same slopes:

  • The lines y = 1/2x - 8 and y = 1/2x + 3 have the same slope of 1/2.
  • The lines y = 1/3x + 4 and y = 1/3x + 4 (which are actually the same line) both have the same slope of 1/3.

Thus, the two lines that are parallel are: y = 1/2x - 8 and y = 1/2x + 3.