Interpretation of linear functions in context is a key concept tested on the SAT Math section. Linear functions are used to model relationships between two variables, such as time and distance, or temperature and humidity. Understanding how to interpret linear functions in realworld contexts is essential for success on the SAT Math section. To help students prepare for this type of question, we have created an SAT practice test that focuses specifically on interpretation of linear functions in context.
As always, should you have any trouble with the questions on this test, don't hesitate to reach out for personalized SAT tutoring to help you ace this section.
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Question 1:
A store offers a discount of $20 per item when a customer purchases more than one item. If the price of one item is $100, which of the following linear equations represents the total cost, C, for purchasing n items, where n > 1?


C = 100n  20

C = 100n  20(n  1)

C = 80n

C = 80n  20
Question 2:
A car rental company charges $50 per day for renting a car and an additional onetime insurance fee of $30. Which of the following linear equations represents the total cost, T, for renting a car for d days?


T = 50d + 30

T = 30d + 50

T = 50d

T = 80d
Question 3:
The cost of a taxi ride is $3 for the first mile and $2 for each additional mile. Which of the following linear equations represents the total cost, C, for a taxi ride of x miles?


C = 3x

C = 3 + 2(x  1)

C = 2x + 1

C = 5x
Question 4:
A company produces Tshirts and sells them for $25 each. It costs the company $5 per Tshirt for materials and an additional $3,000 for equipment. Which of the following linear equations represents the total profit, P, after selling x Tshirts?


P = 25x  5x  3,000

P = 25x  5(x + 3,000)

P = 20x  3,000

P = 20x + 3,000
Question 5:
A student earns $10 per hour at a parttime job. If she earns $100 per week from this job, how many hours did she work per week?


5 hours

10 hours

20 hours

30 hours
Question 6:
A phone company charges a flat rate of $25 per month for basic service and $0.10 per text message. If a customer's total bill was $40 for one month, how many text messages were sent?


150

160

200

250
Question 7:
A company's revenue is represented by the linear function R(x) = 50x, where x is the number of items sold. The company's costs are represented by the linear function C(x) = 30x + 500. What is the breakeven point, where the company's revenue equals its costs?


25 items

30 items

50 items

75 items
Question 8:
A parking garage charges $10 for the first hour and $5 for each additional hour. Which of the following linear equations represents the total cost, C, for parking at the garage for h hours, where h > 1?


C = 10h

C = 10 + 5(h  1)

C = 5h + 5

C = 5h + 10
Question 9:
A factory produces 500 units of a product per day at a cost of $2 per unit. It sells the product for $5 per unit. Which of the following linear equations represents the daily profit, P, after selling x units?


P = 5x  2x

P = 3x  500

P = 3x

P = 2x + 500
Question 10:
A train travels at a constant speed of 60 miles per hour. Which of the following linear equations represents the distance, D, the train has travelled after t hours?


D = 60t

D = 60 + t

D = 60/t

D = t/60
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