Linear Equations: Parallel Lines & Systems of Equations

A park is designed with two paths. Path A has a slope of 2 and passes through the point (1, 3). Path B is parallel to Path A. What is the equation of Path B?

• y = 3x + 1

• y = 2x + c

• y = x + 2

• y = 2x - 1

Two friends are walking towards each other from opposite ends of a straight road. Friend A starts at (0, 0) and walks with a slope of 1. Friend B starts at (10, 0) and walks with a slope of -1. Where do they meet?

• (5, 5)

• (0, 0)

• (7, 3)

• (10, 10)

A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Write the equation representing the total cost (C) in terms of miles driven (m). If another company charges $15 plus $0.75 per mile, how many miles must you drive for the costs to be equal?

• 30 miles

• 20 miles

• 15 miles

• 25 miles

A line passes through the points (2, 5) and (4, 9). Determine the slope of this line. If another line is perpendicular to it and passes through the point (2, 1), what is the equation of the second line?

• y = 2x - 3

• y = -1/2x + 3

• y = 3x + 1

• y = -3/2x + 4

A school is planning to build two new sports fields. Field X is represented by the equation y = 3x + 2, and Field Y is represented by y = -1/3x + 4. Are the fields parallel, perpendicular, or neither?

• neither

• intersecting

• perpendicular

• parallel

A store sells pencils for $0.50 each and erasers for $0.75 each. If a student buys a total of 10 items for $6.00, write a system of equations to represent the situation and solve for the number of pencils and erasers bought.

• 6 pencils and 4 erasers

• 4 pencils and 6 erasers

• 5 pencils and 5 erasers

• 7 pencils and 3 erasers

A line has the equation y = 2x + 1. What is the equation of a line that is parallel to this line and passes through the point (3, 4)?

• y = 2x - 2

• y = 2x + 4

• y = 2x + 3

• y = -2x + 1

Two lines are represented by the equations y = 4x - 1 and y = -1/4x + 2. Are these lines parallel, perpendicular, or neither?

• coincident

• parallel

• perpendicular

• intersecting

A delivery truck travels at a speed of 50 miles per hour. Another truck travels at a speed of 70 miles per hour. If they start from the same point at the same time, how far apart will they be after t hours? Write a system of equations to represent their distances.

• d1 = 60t, d2 = 70t, distance apart = 10t

• d1 = 50t, d2 = 80t, distance apart = 30t

• d1 = 50t, d2 = 70t, distance apart = 30t

• d1 = 50t, d2 = 70t, distance apart = 20t

A farmer has a rectangular field with a length that is twice its width. If the perimeter of the field is 60 meters, write a system of equations to find the dimensions of the field.

• Width: 5 meters, Length: 10 meters

• Width: 10 meters, Length: 20 meters

• Width: 12 meters, Length: 24 meters

• Width: 15 meters, Length: 30 meters