Mastering Parallel & Perpendicular Lines in Real Life

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 + 1

• y = 2x + 3

• y = 3x + 5

• y = 2x - 2

A street runs perpendicular to a riverbank. If the equation of the riverbank is y = -1/2x + 4, what is the slope of the street that is perpendicular to it?

• -1/2

• 2

• -2

• 0

Two friends are standing at points A(2, 3) and B(2, 7) on a coordinate grid. If they walk in a straight line to meet at point C, what type of line do they create, and what is the slope of line AC?

• The line is vertical and the slope of line AC is undefined.

• The line is vertical and the slope of line AC is 1.

• The line is diagonal and the slope of line AC is 2.

• The line is horizontal and the slope of line AC is 0.

A building is designed with windows that are parallel to the ground. If the bottom of the window is at y = 1 and the top is at y = 5, what is the equation of the line representing the bottom of the window?

• y = 5

• y = 0

• y = 3

• y = 1

A bike path is represented by the equation y = 3x - 2. If a new path is to be built that is perpendicular to it and passes through the point (4, 1), what is the equation of the new path?

• y = -3x + 1

• y = -1/3x + 13/3

• y = 1/3x - 5

• y = 3x + 2

A fence is built parallel to a road represented by the equation y = 4x + 1. If the fence is 3 units away from the road, what is the equation of the fence?

• y = 4x - 1

• y = 4x + 7

• y = 4x + 4 and y = 4x - 2

• y = 4x + 1

A line segment connects points D(1, 2) and E(5, 2). What type of line is DE, and how would you graph it?

• DE is a vertical line.

• DE is a diagonal line.

• DE is a horizontal line.

• DE is a curved line.

A school is planning to build a new basketball court that is perpendicular to the existing soccer field. If the soccer field is represented by the equation y = 1/3x + 2, what is the slope of the basketball court?

• -1/3

• 3

• -3

• 1/3

Two lines intersect at point F(3, 4). If one line has a slope of 2, what is the slope of the line that is perpendicular to it?

• -0.5

• -2

• 1

• 0

A city planner is designing two roads that are parallel. If one road is represented by the equation y = -x + 6, what is the equation of the other road that passes through the point (0, 2)?

• y = -x + 4

• y = x + 2

• y = -x + 2

• y = 2x + 6