Linear Equation Word Problems

This problem:

• gives you a rate of change (slope) and a starting point (y-intercept)

• relates two different objects

• gives you a rate of change (slope) and a sample point (x,y)

Suppose a 5-minute overseas call costs $5.91 and a 10-minute call costs $10.86. The cost of the call and the length of the call are related. The cost of each minute is constant. How long can you talk on the phone if you have $12 to spend?

• 11.2 minutes

• 12.8 minutes

• 8.8 minutes

• 21.8 minutes

Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 foot per day. Write an equation to represent the given situation.

• y = -0.5x + 34

• y = -34x + 0.5

• y - 34 = 0.5(x - 1)

• 34x - 0.5y = 33.5

When an individual rides in a taxi for 20 miles, it costs them $21. Another individual rides in the same taxi for 30 miles and pays $26.50. What information is given and which equation should you use?

• A slope and y - intercept is given; use y = mx + b.

• A slope and y - intercept is given; use y - y1 = m(x - x1).

• Two points are given; use y - y1 = m(x - x1).

• Two different items that add to a total are given; use Ax + By = C.

A plumber charges $25 for a service call plus $50 per hour of service. Write an equation for the given situation.

• y = 50x + 25

• y = 25x + 50

• y - 50 = 1(x - 25)

• 25x + 50y = 75

Classroom performance points are worth 0.25 of your overall score and concept checks are worth 0.375 of your overall score. A student has earned 46.25% of their overall grade from these two categories alone. Write an equation to represent the given situation.

• y = 0.25x + 0.375

• y - 0.375 = 0.25(x - 46.25)

• y - 46.25 = 0.25(x - 0.375)

• 0.25x + 0.375y = 46.25

1) A car is driving down from the top of a Colorado mountain. The elevation at the top of the mountain is 13,500 feet. Every minute of driving, the car’s elevation decreases by 150 feet. Write an equation to represent the given situation.

• y = 150x + 13,500

• y = -150x + 13,500

• y - 13,500 = -(x - 150)

• 150x + 13,500y = 13,750

A car rental company charges $164 for renting a vehicle for 2 day. They also charge $198 for renting a vehicle for a total of 4 days. Write an equation to represent the given situation.

• y = 2x + 164

• y - 164 = 17(x - 2)

• y - 198 = 34(x - 4)

• 4x + 164y = 198

The cost to rent a car at the Johnson Car Rental is $29 per day plus a $50 non-refundable insurance cost. Write an equation to represent the given situation.

• y = 29x + 50

• y = 50x + 29

• y - 50 = 1(x - 29)

• 29x + 50y = 79

The Joyner’s swimming pool currently has 30 inches of water in it. In the spring, Mr. Joyner will refill the swimming pool by adding water at a rate of 2 inches per hour. Write an equation to represent the given situation.

• y = -2x + 30

• y = 2x + 30

• y - 30 = 2(x - 0)

• -2x + 30y = 28