How many linear functions questions are on the SAT?

Linear functions sit inside the Algebra domain, which makes up roughly 35 percent of SAT Math. Expect around 2 to 4 questions that lean directly on linear function skills across your two modules.

What is the difference between a linear equation and a linear function?

A linear equation is a statement you solve, like 3x + 5 = 20. A linear function describes a relationship, f(x) = mx + b, and the SAT tests whether you can interpret m and b in context, evaluate the function, and move between its table, graph, and equation forms.

Can I use Desmos on linear function questions?

Yes. Desmos is built into the digital SAT and into Satified. Graphing the function is often the fastest route for intersection and interpretation questions, but you should still be able to read slope and intercept without it.

Is this practice really free?

Yes. Every drill regenerates with fresh numbers each time and there is no account, paywall, or ad.

Why do the questions change their numbers?

Each question is a generator. Practicing the same pattern with new numbers forces you to learn the method instead of memorizing an answer, which is exactly what the real test punishes.

Algebra · Skill 3 of 5

SAT Linear Functions Practice

On the digital SAT, linear functions show up as tables, graphs, word problems, and f(x) notation, and the test moves between those forms on purpose. This page shows you the exact patterns, walks one through completely, then hands you drills that rebuild themselves with fresh numbers every time.

Domain: Algebra
About 35% of the test is Algebra
Difficulty: easy to hard
Free, no account

Drill linear functions now → See all Algebra skills

The patterns the SAT actually uses

Every linear functions question you will see is a costume on one of a small number of patterns. Learn the pattern and the costume stops mattering.

Pattern 01

Interpret m and b in context

A function like C(x) = 12x + 40 models a real cost. The question asks what 12 or 40 means. The slope is always the rate per unit, and the constant is always the starting value.

Pattern 02

Build the function from two points

A table or word problem gives two input and output pairs. You compute the slope from the pairs, then push one point through to find b. Watch for tables that skip x values.

Pattern 03

Evaluate and reverse evaluate

Straightforward f(3) questions, and their reverse: given f(x) = 19, find x. Reverse questions are the same skill with one extra algebra step, and they are graded exactly the same.

Pattern 04

Compare forms of the same function

One function shown as a graph, another as an equation or table, and a question about which grows faster or where they meet. Convert everything to slope and intercept, then compare.

One worked example, start to finish

Worked example · medium

A gym charges a one time enrollment fee plus a flat monthly rate. The total cost after 3 months is $205, and the total cost after 7 months is $385. Which function gives the total cost C(m), in dollars, after m months?

Two month and cost pairs are hiding in the story: (3, 205) and (7, 385).
Slope is change in cost over change in months: (385 − 205) ÷ (7 − 3) = 180 ÷ 4 = 45. The monthly rate is $45.
Push one point through C(m) = 45m + b. Using (3, 205): 205 = 135 + b, so b = 70. The enrollment fee is $70.
Sanity check with the other point: 45 × 7 + 70 = 315 + 70 = 385. It matches.

Answer: C(m) = 45m + 70

Every version of this question works the same way. The gym becomes a phone plan or a printer, the numbers change, the method never does.

Where students lose the point

Swapping rate and starting value. If the answer choices include both 45m + 70 and 70m + 45, that is deliberate. The number multiplying m is always the per unit rate.
Reading a table as consecutive. Tables often jump from x = 2 to x = 5. Dividing the change in y by the number of rows instead of the change in x is the most common table error.
Sign slips on negative slopes. Decreasing contexts like draining tanks and depreciating cars need a negative m. Check that the function actually decreases.
Answering the wrong variable. The algebra gives x, but the question asks for the cost, or the reverse. Reread the final sentence before you commit.

Using Desmos here

For intersection and comparison questions, type both functions into the built in Desmos calculator and read the meeting point straight off the graph. For interpretation questions Desmos will not help, since the test is asking what the numbers mean. Satified includes the same Desmos calculator the real test gives you, so you can practice deciding when it is worth opening.

Why drilling here is different

Satified's linear functions drills are generators, not a fixed list. Each time one loads, it rebuilds itself with new numbers, new contexts, and freshly shuffled answer choices, at easy, medium, and hard difficulty. You can drill this one skill until interpreting a slope feels like reading, and the bank never runs out. Every answer and explanation in the bank of 1,483 questions has been independently verified.

Ready? The drills regenerate forever.

Start this skill free →

Questions students ask

How many linear functions questions are on the SAT?: Linear functions sit inside the Algebra domain, which makes up roughly 35 percent of SAT Math. Expect around 2 to 4 questions that lean directly on this skill across your two modules.
What is the difference between a linear equation and a linear function?: A linear equation is a statement you solve, like 3x + 5 = 20. A linear function describes a relationship, f(x) = mx + b, and the SAT tests whether you can interpret m and b in context, evaluate the function, and move between its table, graph, and equation forms.
Can I use Desmos on these questions?: Yes. Desmos is built into the digital SAT and into Satified. Graphing is often fastest for intersections, but you should still be able to read slope and intercept without it.
Is this practice really free?: Yes. Every drill regenerates with fresh numbers each time and there is no account, paywall, or ad.
Why do the questions change their numbers?: Each question is a generator. Practicing the same pattern with new numbers forces you to learn the method instead of memorizing an answer, which is exactly what the real test punishes.

Keep going

Linear functions lean on the two skills beside them. If tables and slopes felt shaky, start one step earlier.