Study on the flySAT

Study on the fly›SAT›Math › Linear functions

MathFree

Linear functions — SAT practice questions

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.

  • Section: Math 44 questions on the paper
  • 138 practice questions in the app

Sample questions

Question 1

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?

  1. A-7
  2. B5
  3. C7
  4. D21
Show answer

Answer: C — 7

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

Question 2

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

  1. A-11
  2. B-1
  3. C1
  4. D19
Show answer

Answer: B — -1

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

Question 3

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?

  1. A12
  2. B720
  3. C1,2001{,}200
  4. D3,5003{,}500
Show answer

Answer: C — 1,2001{,}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.

Practice 138 Linear functions questions in the app

More SAT topics

Math

Everything on the SAT

Study on the fly is an independent study tool and is not affiliated with, sponsored by, or endorsed by any testing organization, school, or government body.

SAT® is a registered trademark of the College Board, which is not affiliated with, and does not endorse, this product.

All practice questions and passages are original works created for Study on the fly and are not reproduced from any official test.