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Linear functions — SAT practice questions

Practice 138 Linear functions questions in the app

What this topic is

Linear functions on the SAT Math section cover slope, intercepts, and models of the form y equals mx plus b.

Students must evaluate a function, solve for the input that yields a given output, use a known slope and a known point to find another value, and interpret applied models, including converting a scaled variable such as height in hundreds of meters back to meters. Questions are typically short algebraic items or contextual models.

Common traps include swapping slope and intercept, missing a negative slope, and forgetting the unit scale in the stem. Answers are typically a single number, presented as choices or entered by the student.

Sample questions

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Question 1Easier

A linear function pp is defined by p(x)=3x−8p(x)=3x-8. If p(k)=13p(k)=13, what is the value of kk?

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Answer: C — 7

Substitution gives 3k−8=133k-8=13. Adding 8 and then dividing by 3 gives k=7k=7.

Question 2Mid

The linear function qq has slope −2-2, and q(−1)=9q(-1)=9. What is the value of q(4)q(4)?

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Answer: B — −1-1

The input increases by 5 from −1-1 to 4, so the output changes by 5(−2)=−105(-2)=-10. Therefore, q(4)=9−10=−1q(4)=9-10=-1.

Question 3Mid

The function T(a)=21−0.6aT(a)=21-0.6a models the air temperature, in degrees Celsius, at a height of aa hundreds of meters above a reference elevation. At what height, in meters, does the model predict an air temperature of 13.8 degrees Celsius?

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Answer: C — 1,200

Solving 21−0.6a=13.821-0.6a=13.8 gives a=12a=12. Since aa is measured in hundreds of meters, the height is 12(100)=1,20012(100)=1{,}200 meters.

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Practice 138 Linear functions questions in the app

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