Mastering Parallel and Perpendicular Lines in Geometry

A park has two walking paths that run parallel to each other. If one path is represented by the equation y = 2x + 3, what is the equation of another path that is parallel to it and passes through the point (1, 5)?

• y = 2x - 2

• y = 3x + 5

• y = 2x + 3

• y = 2x + 1

A building is designed with a wall that is perpendicular to the ground. If the ground is represented by the line y = 0, what is the slope of the wall if it intersects the ground at the point (2, 0)?

• 1

• undefined

• 0

• -1

Two friends are walking in a straight line. One friend walks along the line y = -3x + 4, while the other walks along a line that is perpendicular to it. What is the slope of the line that the second friend is walking on?

• -1/3

• 1/3

• 2

• 0

A street runs parallel to a river. If the equation of the street is y = 1/2x - 2, what is the equation of a street that is parallel to it and passes through the point (4, 1)?

• y = 1/2x - 1

• y = 1/2x - 3

• y = 1/2x + 2

• y = -1/2x + 1

A skateboard ramp is designed to be perpendicular to the ground. If the ground is represented by the line y = 0, and the ramp's equation is y = 3x - 6, what is the slope of the line that represents the ground?

• 1

• 0

• 2

• -3

A city planner is designing two roads that are perpendicular to each other. If one road is represented by the equation y = 4x + 1, what is the equation of the road that is perpendicular to it and passes through the point (0, -3)?

• y = 1/4x + 3

• y = -4x + 1

• y = -1/4x - 3

• y = 2x - 3

A fence is built parallel to a straight road. If the road is represented by the equation y = -x + 2, what is the equation of the fence that is parallel to the road and passes through the point (3, 1)?

• y = -x + 1

• y = x + 2

• y = -x - 1

• y = -x + 4

A soccer field has two goal lines that are parallel. If one goal line is represented by the equation y = 0, what is the equation of another goal line that is parallel and located 5 units above it?

• y = 10

• y = 2

• y = 5

• y = -5

A river flows in a straight line represented by the equation y = 2x + 1. A bridge is built perpendicular to the river. What is the slope of the bridge?

• 0

• -2

• 1/2

• -1/2

Two lines intersect at a right angle. If one line is represented by the equation y = 1/3x + 2, what is the equation of the line that is perpendicular to it and passes through the point (3, 4)?

• y = -3x + 13

• y = 2x + 1

• y = 1/3x + 4

• y = -1/3x + 5