SAT Math Practice Test: Linear Functions and Models
- Linear Functions and Models
- 10 questions
- 14 minutes
These 10 questions practice building and interpreting linear models, a core part of the SAT Algebra domain. When a question asks what a number means, ask yourself whether it changes with the input (a rate) or stays fixed (a starting value).
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A plumber uses the equation C = 65h + 90 to find the total charge C, in dollars, for a job that takes h hours.
What is the best interpretation of 65 in this context?
Correct answer: C
The coefficient of h is the rate: each extra hour adds $65. The flat fee charged no matter how long the job takes is 90, the constant term.
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Question 2
A line in the xy-plane passes through the points (2, 7) and (6, 19). Which equation defines the line?
Correct answer: A
The slope is (19 − 7) ÷ (6 − 2) = 3, and 7 = 3(2) + b gives b = 1. The choice y = 3x + 7 uses the y-value of a point as the intercept.
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Question 3
A tank holds 480 liters of water. Water drains from the tank at a constant rate of 15 liters per minute.
Which function gives the volume V, in liters, of water left in the tank t minutes after it starts draining?
Correct answer: B
The tank starts at 480 liters and loses 15 liters each minute, so 15t is subtracted from 480. Adding 15t would describe a tank that is filling.
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Question 4
For the linear function f, f(3) = 10 and f(7) = 22. What is the value of f(12)?
Correct answer: D
The slope is (22 − 10) ÷ (7 − 3) = 3, so f(12) = 22 + 3(12 − 7) = 37. The choice 36 is 3 × 12, which ignores the intercept of 1.
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Question 5
A taxi ride costs $3.50 plus $2.25 for each mile driven. A rider paid $21.50 for one ride.
How many miles was the ride?
Correct answer: B
Subtract the starting charge first: 21.50 − 3.50 = 18, and 18 ÷ 2.25 = 8 miles. The choice 9.6 comes from dividing 21.50 by 2.25 without removing the $3.50.
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Question 6
Line k passes through the origin and is perpendicular to the line y = 23x − 4. Which equation defines line k?
Correct answer: D
Perpendicular slopes are negative reciprocals, so the slope of k is −3/2, and a line through the origin has intercept 0. The choice with slope 3/2 takes the reciprocal but forgets to change the sign.
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Question 7
x 0 2 4 y 5 11 17 The table shows three values of x and their corresponding values of y, where y is a linear function of x. Which equation defines this relationship?
Correct answer: A
When x increases by 2, y increases by 6, so the slope is 6 ÷ 2 = 3; when x = 0, y = 5. The choice with slope 6 uses the change in y without dividing by the change in x.
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Question 8
What is the slope of the line with equation 4x + 2y = 10 in the xy-plane?
Correct answer: C
Solving for y gives y = −2x + 5, so the slope is −2. The value 5 is the y-intercept, not the slope.
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Question 9
A streaming service models its number of subscribers S, in thousands, m months after launch with the equation S = 1,200 + 85m.
According to the model, how many more subscribers, in thousands, does the service have after 6 months than after 2 months?
Correct answer: C
The difference is 85 × (6 − 2) = 340 thousand; the 1,200 cancels out. The choice 510 is 85 × 6, the growth since launch rather than since month 2.
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Question 10
Line ℓ in the xy-plane has an x-intercept of 4 and a y-intercept of −6. What is the slope of line ℓ?
Correct answer: D
The line passes through (4, 0) and (0, −6), so the slope is (−6 − 0) ÷ (0 − 4) = 3/2. A negative answer comes from subtracting the coordinates in different orders.
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