Question

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

Answer 1

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.