Slope Equations: Real-World Problems & Line Relationships

A car travels on a straight road that has a slope of 2. If the car starts at the point (0, 0), what is the equation of the line representing the car's path?

• y = 2x

• y = -2x

• y = 2x + 1

• y = x + 2

A bike path is designed to be parallel to a road with a slope of -3. If the bike path passes through the point (1, 4), what is the equation of the bike path?

• y = 3x + 1

• y = -3x + 4

• y = -3x + 10

• y = -3x + 7

Two friends are hiking on different trails. One trail has a slope of 1/2 and passes through the point (2, 3). The other trail has a slope of -2 and passes through (2, 1). Are the trails parallel, perpendicular, or neither?

• parallel

• neither

• perpendicular

• intersecting

A building is being constructed with a roof that has a slope of 4. If the base of the building is at the point (0, 0), what is the equation of the roof?

• y = 4x

• y = x + 4

• y = 2x

• y = 4x + 1

A skateboard ramp is designed to be perpendicular to a flat surface. If the flat surface has a slope of 1/3, what is the slope of the skateboard ramp?

• -3

• 1/3

• 0

• 3

A train travels along a track that has a slope of 5. If the train starts at the point (0, 0), what is the y-coordinate of the train when it reaches x = 3?

• 15

• 5

• 10

• 20

A new road is being built parallel to an existing road with the equation y = -2x + 5. What is the equation of the new road if it passes through the point (3, 1)?

• y = -2x + 3

• y = -2x + 7

• y = -2x + 5

• y = 2x + 1

A line has a slope of -1 and passes through the point (4, 2). What is the equation of this line?

• y = -x + 6

• y = -2x + 8

• y = -x + 4

• y = x + 2

Two lines are represented by the equations y = 3x + 1 and y = -1/3x + 2. Are these lines parallel, perpendicular, or neither?

• intersecting

• parallel

• perpendicular

• coincident

A farmer wants to create a fence that is perpendicular to a line with a slope of 2. If the fence starts at the point (1, 1), what is the slope of the fence?

• 3

• 0

• 1

• -1/2