SAT Linear Functions

Linear functions questions treat a line as a function: evaluating it, finding where it crosses zero, and interpreting slope and intercept in context. When two expressions are set equal, both sides matter — solving only one is the usual slip.

Practise this skill freeHow the SAT is structured
MathAlgebra90 questions
The trap on this skill

Setting only one expression equal to zero instead of setting the two functions equal.

How this skill behaves

What 90 questions on it look like

90% of these questions can appear in the harder second module. On a section-adaptive test that matters: this is a skill that keeps mattering after a strong first module, not one you leave behind.

43% of the bank for this skill is rated hard, so it rewards practice past the point where the basic form feels comfortable.

medium47%
hard43%
easy10%

Difficulty mix across the 90 questions in this skill.

From the bank

Three real linear functions questions

Each one explains the credited answer and why every other option fails.

Algebra · medium

Dockside trial cart fitting tally card tracks two balances after t weeks. Balance A is A(t) = 79 + 6t, and balance B is B(t) = 124 - 2t. For what value of t are the balances equal?

  1. A15/2
  2. B45/2
  3. C45/8correct
  4. D203/8
Why C is correct — and why the others are not

Set the functions equal: 79 + 6t = 124 - 2t. Then 8t = 45, so t = 45/8. That reasoning is tied to the item-specific detail about Linear functions. A final check is testing the value in the original relationship.

A. This value results from setting only one expression equal to zero instead of setting the two functions equal

B. This value results from setting only one expression equal to zero instead of setting the two functions equal

D. This value results from setting only one expression equal to zero instead of setting the two functions equal

Algebra · hard

Classroom final tile planting packing list tracks two balances after t weeks. Balance A is A(t) = 72 + 3t, and balance B is B(t) = 118 - 3t. For what value of t are the balances equal?

  1. A46/3
  2. B95/3
  3. C23/3 + 1
  4. D23/3correct
Why D is correct — and why the others are not

Set the functions equal: 72 + 3t = 118 - 3t. Then 6t = 46, so t = 23/3. This matches the evidence or condition involving Linear functions. A final check is checking the comparison against the baseline value.

A. This value results from setting only one expression equal to zero instead of setting the two functions equal

B. This value results from setting only one expression equal to zero instead of setting the two functions equal

C. This value results from setting only one expression equal to zero instead of setting the two functions equal

Algebra · easy

Bookshop south mural scanning stock card tracks two balances after t weeks. Balance A is A(t) = 43 + 3t, and balance B is B(t) = 86 - 2t. For what value of t are the balances equal?

  1. A43/3
  2. B43/2
  3. C43/5correct
  4. D129/5
Why C is correct — and why the others are not

Set the functions equal: 43 + 3t = 86 - 2t. Then 5t = 43, so t = 43/5. This is the only choice that stays consistent with the detail about Linear functions. A final check is verifying the sign and size of the result.

A. This value results from setting only one expression equal to zero instead of setting the two functions equal

B. This value results from setting only one expression equal to zero instead of setting the two functions equal

D. This value results from setting only one expression equal to zero instead of setting the two functions equal

90 questions on this skill, free to start.

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FAQ

Linear Functions questions

What does the slope mean in a context question?

The rate of change per unit — how much the output moves for each unit increase in the input, in the units the problem states.

How do I find where a function equals zero?

Set the whole expression equal to zero and solve. If two expressions are set equal to each other, move everything to one side first.
Last reviewed 2026-08-28. Format and scoring facts sourced to College Board. Question counts describe the PrepScore bank, not the exam.
Same domain
Systems of Linear Equations135 questionsLinear Equations in One Variable128 questionsLinear Equations in Two Variables127 questionsLinear Modeling / Word Problems124 questions

Practise linear functions until the trap stops working.

Real Digital SAT questions, the reasoning on every option, and a mistake bank that only clears when you get it right.

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