Interpretation of Linear Functions in Context

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 real-world 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?

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1. C = 100n - 20

2. C = 100n - 20(n - 1)

3. C = 80n

4. C = 80n - 20

Question 2:

A car rental company charges $50 per day for renting a car and an additional one-time insurance fee of $30. Which of the following linear equations represents the total cost, T, for renting a car for d days?

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1. T = 50d + 30

2. T = 30d + 50

3. T = 50d

4. 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?

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1. C = 3x

2. C = 3 + 2(x - 1)

3. C = 2x + 1

4. C = 5x

Question 4:

A company produces T-shirts and sells them for $25 each. It costs the company $5 per T-shirt for materials and an additional $3,000 for equipment. Which of the following linear equations represents the total profit, P, after selling x T-shirts?

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1. P = 25x - 5x - 3,000

2. P = 25x - 5(x + 3,000)

3. P = 20x - 3,000

4. P = 20x + 3,000

Question 5:

A student earns $10 per hour at a part-time job. If she earns $100 per week from this job, how many hours did she work per week?

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1. 5 hours

2. 10 hours

3. 20 hours

4. 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?

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1. 150

2. 160

3. 200

4. 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 break-even point, where the company's revenue equals its costs?

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1. 25 items

2. 30 items

3. 50 items

4. 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?

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1. C = 10h

2. C = 10 + 5(h - 1)

3. C = 5h + 5

4. 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?

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1. P = 5x - 2x

2. P = 3x - 500

3. P = 3x

4. 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?

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1. D = 60t

2. D = 60 + t

3. D = 60/t

4. D = t/60

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