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Determine whether the lines in each question are parallel, perpendicular, or neither.

1. a) y = 2x + 1
b) 2x + y = 7
2. a) y = -4x + 1
b) 4x + y = -3

User Rkusa
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1 Answer

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Final answer:

By comparing the slopes of the given equations, we determined that the first pair of lines are perpendicular, and the second pair of lines are parallel.

Step-by-step explanation:

To determine whether two lines are parallel, perpendicular, or neither, you can compare their slopes. The slope of a line given by the equation y = mx + b is m. If two lines are parallel, they have the same slope. If they are perpendicular, the slopes of the lines are negative reciprocals of each other.

For the first pair of equations:

  • a) y = 2x + 1 has a slope of 2.
  • b) To express 2x + y = 7 in the y = mx + b form, rearrange it to get y = -2x + 7, which has a slope of -2.

Since the slopes are negative reciprocals, the lines are perpendicular.

For the second pair of equations:

  • a) y = -4x + 1 has a slope of -4.
  • b) To express 4x + y = -3 in the y = mx + b form, rearrange it to get y = -4x - 3, which has a slope of -4.

The slopes are equal, implying that the lines are parallel.

User Avi Pinto
by
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