Heart of Algebra

Linear Functions and Their Graphs

Interpret slope, intercepts, and the meaning of linear functions in context. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on linear functions and their graphs is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 A gym charges a monthly fee of $34 plus $5 per visits. Which equation gives the total cost y for x v… easy 400-500 Open
2 A plumber charges a service call fee of $22 plus $9 per hours. Which equation gives the total bill y… easy 400-500 Open
3 A phone plan charges a monthly base of $14 plus $13 per gigabytes used. Which equation gives the mon… easy 400-500 Open
4 A rideshare charges a pickup fee of $50 plus $8 per miles. Which equation gives the fare y for x mil… easy 400-500 Open
5 A printer charges a setup charge of $22 plus $14 per pages. Which equation gives the order cost y fo… easy 400-500 Open
6 A gym charges a monthly fee of $15 plus $5 per visits. Which equation gives the total cost y for x v… easy 400-500 Open
7 A plumber charges a service call fee of $7 plus $15 per hours. Which equation gives the total bill y… easy 500-600 Open
8 A phone plan charges a monthly base of $8 plus $3 per gigabytes used. Which equation gives the month… easy 500-600 Open
9 A rideshare charges a pickup fee of $13 plus $15 per miles. Which equation gives the fare y for x mi… medium 500-600 Open
10 A printer charges a setup charge of $45 plus $4 per pages. Which equation gives the order cost y for… medium 500-600 Open
11 A gym charges a monthly fee of $49 plus $9 per visits. Which equation gives the total cost y for x v… medium 500-600 Open
12 A plumber charges a service call fee of $17 plus $12 per hours. Which equation gives the total bill … medium 500-600 Open
13 A phone plan charges a monthly base of $34 plus $6 per gigabytes used. Which equation gives the mont… medium 600-700 Open
14 A rideshare charges a pickup fee of $27 plus $11 per miles. Which equation gives the fare y for x mi… medium 600-700 Open
15 A printer charges a setup charge of $37 plus $10 per pages. Which equation gives the order cost y fo… medium 600-700 Open
16 A gym charges a monthly fee of $44 plus $6 per visits. Which equation gives the total cost y for x v… medium 600-700 Open
17 A plumber charges a service call fee of $19 plus $10 per hours. Which equation gives the total bill … medium 600-700 Open
18 A phone plan charges a monthly base of $28 plus $12 per gigabytes used. Which equation gives the mon… medium 600-700 Open
19 A rideshare charges a pickup fee of $44 plus $6 per miles. Which equation gives the fare y for x mil… hard 600-700 Open
20 A printer charges a setup charge of $28 plus $6 per pages. Which equation gives the order cost y for… hard 700-800 Open
21 A gym charges a monthly fee of $24 plus $8 per visits. Which equation gives the total cost y for x v… hard 700-800 Open
22 A plumber charges a service call fee of $22 plus $11 per hours. Which equation gives the total bill … hard 700-800 Open
23 A phone plan charges a monthly base of $21 plus $13 per gigabytes used. Which equation gives the mon… hard 700-800 Open
24 A rideshare charges a pickup fee of $22 plus $5 per miles. Which equation gives the fare y for x mil… hard 700-800 Open
25 A printer charges a setup charge of $18 plus $3 per pages. Which equation gives the order cost y for… hard 700-800 Open