Real-Life Linear Equations: Parallel Lines & Word Problems

A park has two walking paths. Path A runs parallel to Path B. If Path A can be represented by the equation y = 2x + 3, what is the equation of Path B?

• y = 2x - 1

• y = 2x + 3

• y = 2x + b (where b is a constant different from 3)

• y = 3x + 3

A car rental company charges a flat fee of $20 plus $0.50 per mile driven. Write the equation that represents the total cost (C) of renting a car for x miles.

• C = 20 - 0.50x

• C = 20 + 0.50x

• C = 20 + 0.75x

• C = 0.50x + 10

Two friends are walking in a straight line. Friend A walks at a speed of 3 miles per hour, while Friend B walks at a speed of 5 miles per hour. Write an equation to represent the distance each friend travels after t hours.

• Distance_A = 3t, Distance_B = 4t

• Distance_A = 4t, Distance_B = 6t

• Distance_A = 2t, Distance_B = 5t

• Distance_A = 3t, Distance_B = 5t

A school is planning to build a new basketball court. The line representing the length of the court is 2 feet longer than twice the width. If the width is represented by w, write the equation for the length.

• l = 2w - 2

• l = 2w + 2

• l = 3w + 2

• l = w + 2

A delivery truck travels at a speed of 60 miles per hour. If it travels for t hours, write an equation for the distance (d) it covers.

• d = 60 + t

• d = 30t

• d = 60t^2

• d = 60t

A gardener is planting flowers in a rectangular garden. The length of the garden is 4 feet longer than the width. If the width is represented by w, write the equation for the length of the garden.

• l = w + 2

• l = 4w

• l = w - 4

• l = w + 4

Two lines are represented by the equations y = 3x + 1 and y = -1/3x + 4. Are these lines parallel, perpendicular, or neither?

• perpendicular

• coincident

• parallel

• intersecting

A train travels 80 miles in 2 hours. Write an equation that represents the relationship between distance (d), rate (r), and time (t).

• d = 60t

• d = 80t

• d = 20t

• d = 40t

A store sells notebooks for $2 each and pens for $1 each. If a student buys a total of 10 items for $14, write an equation to represent the relationship between the number of notebooks (n) and pens (p).

• n + p = 8 and 2n + p = 16

• n + p = 10 and 2n + p = 14

• n + p = 10 and 2n + p = 12

• n + p = 12 and 2n + p = 10

A bike rental shop charges a one-time fee of $15 and $2 for each hour rented. Write the equation that represents the total cost (C) for h hours of rental.

• C = 2h - 15

• C = 15 - 2h

• C = 15 + 2h

• C = 15h + 2