Quick Answer
SAT linear functions practice questions test how well you can connect equations, tables, graphs, slope, intercepts, rates of change, and real-world models. This page includes 65 SAT-style linear function questions with answer choices, full solutions, and trap notes. The questions begin with basic function evaluation and move into harder model-building, equivalent equation, and parameter questions.
What to Know Before You Start
- A linear function has a constant rate of change. Every time x increases by the same amount, y changes by the same amount.
- The most common SAT form is y = mx + b, where m is slope and b is the y-intercept.
- Function notation such as f(4) asks for the output when the input is 4.
- In word problems, the starting value usually becomes the intercept, and the repeated change usually becomes the slope.
- The SAT often hides linear functions inside tables, real-world situations, equivalent equations, and graph descriptions.
- Many wrong answers come from swapping slope and intercept, missing a negative sign, or using the y-value at x = 1 as the y-intercept.
In This Guide – 65 SAT Linear Functions Practice Questions
- What does the SAT test in linear functions?
- How do SAT linear function questions test basic evaluation?
- How do you handle slope, rate of change, and intercepts?
- How are linear functions used in SAT word problems?
- How do you move between different forms of linear functions?
- What do hard SAT linear function questions look like?
- What mistakes cost students points on linear functions?
- How should you study SAT linear functions in 2 weeks?
- Frequently asked questions
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What Does the SAT Test in Linear Functions?
Linear functions are part of the SAT Math Algebra domain. On the Digital SAT, they may appear as direct function notation, an equation in slope-intercept form, a table with a constant rate of change, a real-world model, or an equivalent equation that needs to be rearranged. The math is not usually long, but the question wording often forces you to identify what the slope and intercept actually mean.
A strong SAT student does three things before solving: names the input, names the output, and identifies the rate of change. Once those three pieces are clear, most linear function questions become short algebra problems instead of confusing word problems.
| SAT Linear Function Skill | What It Tests | Common Trap | Practice Set |
|---|---|---|---|
| Function evaluation | Substituting inputs and working backward from outputs | Confusing input with output | Q1-Q15 |
| Slope and intercepts | Rate of change, x-intercept, y-intercept, and line forms | Swapping slope and intercept | Q16-Q30 |
| Linear models | Translating real-world situations into functions | Multiplying the fixed cost by the input | Q31-Q45 |
| Equivalent forms | Rearranging equations and matching representations | Rejecting equivalent equations because they look different | Q46-Q55 |
| Hard mixed questions | Parameters, unknown inputs, comparisons, and multi-step models | Solving before understanding the function relationship | Q56-Q65 |
SAT strategy: Before using the calculator, ask: What is the starting value? What changes each time x increases by 1? What is the question actually asking for – an input, an output, a slope, or an intercept?
Download SAT Math Topic Wise Practice Questions
Practice x-intercepts, y-intercepts, linear functions, equations, graphs, and SAT Math topic-wise question sets in one place.
Download Math Practice QuestionsHow Do SAT Linear Function Questions Test Basic Evaluation?
Start with input and output. These questions check whether you can substitute correctly, read function notation, and recognize a constant rate of change from an equation or table.
BASIC LINEAR FUNCTION EVALUATION
EASY
Question 1
If f(x) = 3x + 7, what is the value of f(4)?
A) 16
B) 19
C) 21
D) 28
Show full solution
Correct answer: B) 19
Substitute 4 for x: f(4) = 3(4) + 7 = 12 + 7 = 19.
SAT trap: The input replaces x only. Do not add the input to the constant or stop after multiplying.
BASIC LINEAR FUNCTION EVALUATION
EASY
Question 2
If g(x) = -2x + 5, what is the value of g(-3)?
A) -1
B) 1
C) 11
D) 13
Show full solution
Correct answer: C) 11
g(-3) = -2(-3) + 5 = 6 + 5 = 11.
SAT trap: Negative inputs are where careless sign mistakes happen. Use parentheses around the substituted value.
BASIC LINEAR FUNCTION EVALUATION
EASY
Question 3
If h(t) = (1/2)t – 4, what is h(10)?
A) 1
B) 5
C) 6
D) 14
Show full solution
Correct answer: A) 1
h(10) = (1/2)(10) – 4 = 5 – 4 = 1.
SAT trap: The fraction is a multiplier. The SAT often uses simple fractions to check whether you follow the full rule.
BASIC LINEAR FUNCTION EVALUATION
EASY
Question 4
If f(x) = 5x – 9 and f(a) = 16, what is the value of a?
A) 3
B) 4
C) 5
D) 7
Show full solution
Correct answer: C) 5
Set the output equal to 16: 5a – 9 = 16. Then 5a = 25, so a = 5.
SAT trap: This is a working-backward question, not an evaluation at x = 16.
BASIC LINEAR FUNCTION EVALUATION
MEDIUM
Question 5
If f(x) = 4 – 3x, what is f(2) – f(-1)?
A) -9
B) -5
C) 5
D) 9
Show full solution
Correct answer: A) -9
f(2) = 4 – 6 = -2. f(-1) = 4 – 3(-1) = 7. So f(2) – f(-1) = -2 – 7 = -9.
SAT trap: When subtracting a function value, subtract the entire second value.
BASIC LINEAR FUNCTION EVALUATION
EASY
Question 6
A linear function has the values shown: when x is 0, y is 5; when x is 1, y is 8; when x is 2, y is 11. Which equation represents the function?
A) y = 2x + 5
B) y = 3x + 5
C) y = 5x + 3
D) y = 8x + 5
Show full solution
Correct answer: B) y = 3x + 5
The output increases by 3 each time x increases by 1, so the slope is 3. Since y = 5 when x = 0, the equation is y = 3x + 5.
SAT trap: The y-value at x = 1 is not the y-intercept. Look at x = 0 for the intercept.
BASIC LINEAR FUNCTION EVALUATION
MEDIUM
Question 7
A line passes through (0, -4) and has a slope of 6. What is the value of y when x = 3?
A) 10
B) 12
C) 14
D) 18
Show full solution
Correct answer: C) 14
The equation is y = 6x – 4. At x = 3, y = 18 – 4 = 14.
SAT trap: The intercept is negative 4. Keeping the sign correct is the whole question.
BASIC LINEAR FUNCTION EVALUATION
MEDIUM
Question 8
If f(x) = ax + 2 and f(5) = 17, what is the value of a?
A) 2
B) 3
C) 4
D) 5
Show full solution
Correct answer: B) 3
Substitute x = 5: 5a + 2 = 17. Then 5a = 15, so a = 3.
SAT trap: The coefficient a is the rate of change, not the output value.
BASIC LINEAR FUNCTION EVALUATION
MEDIUM
Question 9
A linear function f has f(0) = 4 and f(3) = 13. What is f(7)?
A) 21
B) 23
C) 25
D) 29
Show full solution
Correct answer: C) 25
The slope is (13 – 4)/(3 – 0) = 3. So f(x) = 3x + 4 and f(7) = 25.
SAT trap: The output change of 9 happens over 3 input units. Divide before extending the pattern.
BASIC LINEAR FUNCTION EVALUATION
HARD
Question 10
If f(x + 2) = 3x + 8 for all values of x, what is f(5)?
A) 11
B) 14
C) 17
D) 23
Show full solution
Correct answer: C) 17
To make the input x + 2 equal 5, set x + 2 = 5, so x = 3. Then f(5) = 3(3) + 8 = 17.
SAT trap: Match the input inside f first. Do not plug 5 into the x on the right side directly.
BASIC LINEAR FUNCTION EVALUATION
EASY
Question 11
A line passes through (0, -6) and (2, 0). What is y when x = 4?
A) 3
B) 6
C) 8
D) 12
Show full solution
Correct answer: B) 6
The slope is (0 – (-6))/(2 – 0) = 3. The line is y = 3x – 6, so at x = 4, y = 6.
SAT trap: The point (2, 0) is the x-intercept, not the y-intercept.
BASIC LINEAR FUNCTION EVALUATION
EASY
Question 12
For the function y = -4x + 10, by how much does y change when x increases by 3?
A) -12
B) -4
C) 3
D) 12
Show full solution
Correct answer: A) -12
The slope is -4, so a 3-unit increase in x changes y by 3(-4) = -12.
SAT trap: The intercept affects starting value, not change. Slope controls change.
BASIC LINEAR FUNCTION EVALUATION
MEDIUM
Question 13
If f(x) = 7 – (1/2)x, for what value of x is f(x) = 1?
A) 6
B) 10
C) 12
D) 16
Show full solution
Correct answer: C) 12
Set 7 – (1/2)x = 1. Then -(1/2)x = -6, so x = 12.
SAT trap: Dividing by negative one half is the same as multiplying by negative 2.
BASIC LINEAR FUNCTION EVALUATION
MEDIUM
Question 14
A linear function has f(2) = 9 and f(6) = 21. What is f(10)?
A) 27
B) 30
C) 33
D) 36
Show full solution
Correct answer: C) 33
The slope is (21 – 9)/(6 – 2) = 3. From x = 6 to x = 10, y increases by 12, so f(10) = 33.
SAT trap: You can extend the slope pattern without finding the full equation.
BASIC LINEAR FUNCTION EVALUATION
HARD
Question 15
If f(x) = 2.5x + 6, what is f(-4)?
A) -16
B) -10
C) -4
D) 4
Show full solution
Correct answer: C) -4
f(-4) = 2.5(-4) + 6 = -10 + 6 = -4.
SAT trap: Decimals do not change the algebra. Keep the sign and multiplication clear.
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How Do You Handle Slope, Rate of Change, and Intercepts on the SAT?
These questions focus on slope, y-intercept, x-intercept, parallel lines, and rate of change. They are common because they connect equations, tables, graphs, and real-world situations.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 16
What is the slope of the line passing through (2, 5) and (6, 17)?
A) 2
B) 3
C) 4
D) 6
Show full solution
Correct answer: B) 3
Slope = (17 – 5)/(6 – 2) = 12/4 = 3.
SAT trap: Slope is change in y divided by change in x, not the other way around.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 17
A line has slope -2 and y-intercept 7. Which equation represents the line?
A) y = 7x – 2
B) y = -2x + 7
C) y = 2x – 7
D) y = -7x + 2
Show full solution
Correct answer: B) y = -2x + 7
Slope-intercept form is y = mx + b. With m = -2 and b = 7, the equation is y = -2x + 7.
SAT trap: Students often swap the slope and intercept. The coefficient of x is the slope.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 18
What is the y-intercept of the line y = 4x – 9?
A) -9
B) -4
C) 4
D) 9
Show full solution
Correct answer: A) -9
In y = mx + b, the y-intercept is b. Here b = -9.
SAT trap: The sign belongs to the intercept. The answer is -9, not 9.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 19
What is the x-intercept of the line 2x + 5y = 20?
A) 4
B) 5
C) 10
D) 20
Show full solution
Correct answer: C) 10
At the x-intercept, y = 0. So 2x = 20 and x = 10.
SAT trap: For the x-intercept, set y equal to zero. For the y-intercept, set x equal to zero.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
MEDIUM
Question 20
What is the slope of the line 3x + 2y = 12?
A) -3/2
B) -2/3
C) 2/3
D) 3/2
Show full solution
Correct answer: A) -3/2
Solve for y: 2y = -3x + 12, so y = (-3/2)x + 6. The slope is -3/2.
SAT trap: In standard form, the slope is -A/B. The negative sign matters.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 21
Which equation has slope 5 and y-intercept -1?
A) y = -x + 5
B) y = 5x – 1
C) y = x – 5
D) y = -5x + 1
Show full solution
Correct answer: B) y = 5x – 1
Using y = mx + b, m = 5 and b = -1, so y = 5x – 1.
SAT trap: The y-intercept is the constant term, not the coefficient of x.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
MEDIUM
Question 22
A line has slope 2 and passes through (4, 9). Which equation represents the line?
A) y = 2x + 1
B) y = 2x + 4
C) y = 4x + 2
D) y = 9x + 2
Show full solution
Correct answer: A) y = 2x + 1
Use y = 2x + b. Substitute (4, 9): 9 = 8 + b, so b = 1. The line is y = 2x + 1.
SAT trap: A point on the line is not automatically an intercept.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 23
A rental cost is modeled by C(n) = 12 + 8n, where n is the number of hours. What does the 8 represent?
A) The starting fee
B) The total cost for 8 hours
C) The cost per additional hour
D) The number of rentals
Show full solution
Correct answer: C) The cost per additional hour
The coefficient of n is the rate of change. Each additional hour adds $8.
SAT trap: The 12 is the starting fee. The 8 is the hourly rate.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 24
A cup of tea starts at 70 degrees and cools by 3 degrees per minute. Which function gives the temperature T after m minutes?
A) T = 70 + 3m
B) T = 70 – 3m
C) T = 3m – 70
D) T = 70m – 3
Show full solution
Correct answer: B) T = 70 – 3m
The starting temperature is 70 and the temperature decreases by 3 each minute, so T = 70 – 3m.
SAT trap: The word cools signals a negative rate of change.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
MEDIUM
Question 25
For a linear function, f(2) = 10 and f(8) = 25. What is the slope?
A) 2
B) 2.5
C) 3
D) 7.5
Show full solution
Correct answer: B) 2.5
Slope = (25 – 10)/(8 – 2) = 15/6 = 2.5.
SAT trap: The output change is 15, but the input changes by 6.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
MEDIUM
Question 26
Which equation represents a line parallel to y = -4x + 3 that passes through (1, 2)?
A) y = -4x + 6
B) y = 4x – 2
C) y = -3x + 5
D) y = x – 4
Show full solution
Correct answer: A) y = -4x + 6
Parallel lines have the same slope, so y = -4x + b. Substitute (1, 2): 2 = -4 + b, so b = 6.
SAT trap: Parallel means same slope, not same intercept.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
HARD
Question 27
A line is perpendicular to y = (1/2)x + 4 and passes through (3, 5). Which equation represents the line?
A) y = -2x + 11
B) y = 2x – 1
C) y = -(1/2)x + 6.5
D) y = (1/2)x + 3.5
Show full solution
Correct answer: A) y = -2x + 11
The perpendicular slope to 1/2 is -2. Use y = -2x + b and substitute (3, 5): 5 = -6 + b, so b = 11.
SAT trap: Perpendicular slopes are negative reciprocals.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
EASY
Question 28
What is the x-intercept of y = -0.5x + 6?
A) 3
B) 6
C) 9
D) 12
Show full solution
Correct answer: D) 12
Set y = 0: 0 = -0.5x + 6. Then 0.5x = 6, so x = 12.
SAT trap: The x-intercept is not the constant term. It is where y equals zero.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
MEDIUM
Question 29
A line has x-intercept 4 and y-intercept -8. Which equation represents the line?
A) y = 2x – 8
B) y = -2x + 8
C) y = 4x – 8
D) y = -8x + 4
Show full solution
Correct answer: A) y = 2x – 8
The intercepts are (4, 0) and (0, -8). The slope is 8/4 = 2, and the y-intercept is -8, so y = 2x – 8.
SAT trap: A y-intercept of -8 means the line crosses below the origin.
SLOPE, RATE OF CHANGE, AND INTERCEPTS
MEDIUM
Question 30
A table for a linear function shows x-values 0, 2, and 4 and y-values 1, 7, and 13. What is the slope?
A) 2
B) 3
C) 6
D) 12
Show full solution
Correct answer: B) 3
From x = 0 to x = 2, y changes from 1 to 7. The slope is 6/2 = 3.
SAT trap: Equal jumps in y must be divided by equal jumps in x.
How Are Linear Functions Used in SAT Word Problems?
In SAT word problems, the starting value is usually the intercept and the repeated change is usually the slope. The key is translating words into a clean equation before solving.
LINEAR FUNCTION WORD PROBLEMS
EASY
Question 31
A streaming plan charges $12 per month plus $3 for each rented movie. Which function gives the monthly cost C for m rented movies?
A) C = 3 + 12m
B) C = 12 + 3m
C) C = 15m
D) C = 12m + 3
Show full solution
Correct answer: B) C = 12 + 3m
The fixed monthly charge is 12, and each movie adds 3 dollars. So C = 12 + 3m.
SAT trap: Fixed costs are intercepts. Per-item costs are slopes.
LINEAR FUNCTION WORD PROBLEMS
EASY
Question 32
A taxi ride costs $4 plus $2.50 per mile. What is the cost of a 12-mile ride?
A) $30
B) $32
C) $34
D) $36
Show full solution
Correct answer: C) $34
Cost = 4 + 2.50(12) = 4 + 30 = 34 dollars.
SAT trap: The starting fee is charged once, not once per mile.
LINEAR FUNCTION WORD PROBLEMS
EASY
Question 33
A student has $80 saved and adds $15 each week. How much money will the student have after 10 weeks?
A) $95
B) $150
C) $200
D) $230
Show full solution
Correct answer: D) $230
Savings = 80 + 15(10) = 80 + 150 = 230 dollars.
SAT trap: The starting amount remains in the total.
LINEAR FUNCTION WORD PROBLEMS
MEDIUM
Question 34
A gym charges a $45 sign-up fee and $20 per month. If a member has paid $165 total, for how many months has the member paid?
A) 4
B) 5
C) 6
D) 8
Show full solution
Correct answer: C) 6
Set 45 + 20m = 165. Then 20m = 120, so m = 6.
SAT trap: Subtract the one-time fee before dividing by the monthly cost.
LINEAR FUNCTION WORD PROBLEMS
EASY
Question 35
A water tank contains 500 gallons and loses 25 gallons per minute. How much water is left after 8 minutes?
A) 200 gallons
B) 275 gallons
C) 300 gallons
D) 475 gallons
Show full solution
Correct answer: C) 300 gallons
Water left = 500 – 25(8) = 500 – 200 = 300 gallons.
SAT trap: The word loses signals a negative rate.
LINEAR FUNCTION WORD PROBLEMS
EASY
Question 36
A bus travels at a constant speed of 55 miles per hour. Which function gives the distance d after t hours?
A) d = 55t
B) d = t + 55
C) d = 55 – t
D) d = 55/t
Show full solution
Correct answer: A) d = 55t
Distance equals rate times time, so d = 55t.
SAT trap: With no starting distance, the intercept is zero.
LINEAR FUNCTION WORD PROBLEMS
MEDIUM
Question 37
A freelancer charges a $120 project fee plus $35 per hour. What is the total charge for 6 hours of work?
A) $210
B) $255
C) $330
D) $420
Show full solution
Correct answer: C) $330
Total = 120 + 35(6) = 120 + 210 = 330 dollars.
SAT trap: Only the hourly rate is multiplied by hours.
LINEAR FUNCTION WORD PROBLEMS
MEDIUM
Question 38
A phone battery is at 100% and loses 7 percentage points per hour. After how many hours will the battery be at 44%?
A) 6
B) 7
C) 8
D) 9
Show full solution
Correct answer: C) 8
Set 100 – 7h = 44. Then -7h = -56 and h = 8.
SAT trap: The battery loses 56 percentage points at 7 points per hour.
LINEAR FUNCTION WORD PROBLEMS
MEDIUM
Question 39
A printer has already printed 20 pages and then prints 24 pages per minute. Which function gives total pages P after m more minutes?
A) P = 24m
B) P = 20m + 24
C) P = 20 + 24m
D) P = 44m
Show full solution
Correct answer: C) P = 20 + 24m
The starting value is 20 pages and the rate is 24 pages per minute, so P = 20 + 24m.
SAT trap: Already printed pages are the intercept.
LINEAR FUNCTION WORD PROBLEMS
EASY
Question 40
A club has 120 members and gains 18 new members each month. How many members will it have after 5 months?
A) 138
B) 190
C) 210
D) 228
Show full solution
Correct answer: C) 210
Members = 120 + 18(5) = 120 + 90 = 210.
SAT trap: Do not replace the starting number with the monthly increase.
LINEAR FUNCTION WORD PROBLEMS
MEDIUM
Question 41
A concert venue charges $15 per student ticket and a $200 reservation fee. Which function gives the total cost T for s students?
A) T = 15s + 200
B) T = 200s + 15
C) T = 215s
D) T = 200 – 15s
Show full solution
Correct answer: A) T = 15s + 200
Each student adds $15, and the fixed fee is $200. The function is T = 15s + 200.
SAT trap: The per-student cost is the slope.
LINEAR FUNCTION WORD PROBLEMS
EASY
Question 42
A machine prints 24 pages each minute. How many pages does it print in 5 minutes?
A) 29
B) 96
C) 120
D) 240
Show full solution
Correct answer: C) 120
P = 24m. For 5 minutes, P = 24(5) = 120.
SAT trap: A constant rate with no starting amount is a direct variation.
LINEAR FUNCTION WORD PROBLEMS
HARD
Question 43
Plan A costs $20 plus $5 per session. Plan B costs $50 plus $2 per session. After how many sessions do the plans cost the same?
A) 6
B) 8
C) 10
D) 12
Show full solution
Correct answer: C) 10
Set 20 + 5s = 50 + 2s. Then 3s = 30, so s = 10.
SAT trap: When comparing two plans, set the expressions equal.
LINEAR FUNCTION WORD PROBLEMS
MEDIUM
Question 44
A candle is 12 inches tall and burns down by 0.8 inch per hour. What is its height after 5 hours?
A) 4 inches
B) 6 inches
C) 8 inches
D) 10 inches
Show full solution
Correct answer: C) 8 inches
Height = 12 – 0.8(5) = 12 – 4 = 8 inches.
SAT trap: The decrease over 5 hours is 4 inches, not 0.8 inch.
LINEAR FUNCTION WORD PROBLEMS
MEDIUM
Question 45
A class trip costs $120 for bus rental plus $18 per student. If the total cost is $480, how many students are going?
A) 15
B) 18
C) 20
D) 24
Show full solution
Correct answer: C) 20
Set 120 + 18s = 480. Then 18s = 360, so s = 20.
SAT trap: Remove the fixed cost first, then divide by the per-student cost.
Need a Faster SAT Math Score Improvement Plan?
Practice questions help most when they are connected to a weekly score plan. Use TestPrepKart’s SAT prep support for live classes, mock tests, error review, and targeted math practice.
How Do You Move Between Different Forms of Linear Functions?
The SAT often gives the same linear function in different forms. You may need to rearrange, compare slopes, use intercepts, or decide whether a table is truly linear.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
EASY
Question 46
Which equation is equivalent to 2y – 6x = 10?
A) y = 3x + 5
B) y = -3x + 5
C) y = 6x + 10
D) y = 3x – 5
Show full solution
Correct answer: A) y = 3x + 5
Add 6x to both sides: 2y = 6x + 10. Divide by 2 to get y = 3x + 5.
SAT trap: Divide every term by 2, not only the y-term.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
MEDIUM
Question 47
Which equation represents the line through (3, 1) and (5, 9)?
A) y = 2x – 5
B) y = 4x – 11
C) y = 4x + 11
D) y = -4x + 13
Show full solution
Correct answer: B) y = 4x – 11
The slope is (9 – 1)/(5 – 3) = 4. Use y = 4x + b and substitute (3, 1): 1 = 12 + b, so b = -11.
SAT trap: A slope of 4 does not make the intercept 4.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
EASY
Question 48
Which function increases the fastest as x increases?
A) f(x) = 2x + 9
B) g(x) = 5x – 1
C) h(x) = -6x + 20
D) p(x) = 3x + 4
Show full solution
Correct answer: B) g(x) = 5x – 1
The fastest increasing function has the greatest positive slope. The slopes are 2, 5, -6, and 3, so g increases fastest.
SAT trap: A large negative slope means fast decrease, not fast increase.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
MEDIUM
Question 49
Which set of y-values would make the table linear if the x-values are 1, 2, 3, and 4?
A) 4, 7, 10, 13
B) 4, 7, 11, 16
C) 4, 8, 12, 17
D) 4, 9, 11, 15
Show full solution
Correct answer: A) 4, 7, 10, 13
For equally spaced x-values, a linear function has equal first differences. The values 4, 7, 10, 13 increase by 3 each time.
SAT trap: One irregular jump breaks the linear pattern.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
HARD
Question 50
For a linear function f, f(x + 1) – f(x) = 7 for all x. What is the slope of f?
A) 1
B) 6
C) 7
D) 14
Show full solution
Correct answer: C) 7
A 1-unit increase in input changes the output by the slope. Since f(x + 1) – f(x) = 7, the slope is 7.
SAT trap: This expression gives the rate directly.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
MEDIUM
Question 51
If f(x) = 6x – 4, what is f(x) – f(x – 2)?
A) -12
B) -8
C) 8
D) 12
Show full solution
Correct answer: D) 12
f(x – 2) = 6(x – 2) – 4 = 6x – 16. Then f(x) – f(x – 2) = (6x – 4) – (6x – 16) = 12.
SAT trap: Subtract the entire second expression, not just its first term.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
HARD
Question 52
A line has y-intercept 5 and x-intercept -2. Which equation represents the line?
A) y = (5/2)x + 5
B) y = -(5/2)x + 5
C) y = 5x – 2
D) y = -2x + 5
Show full solution
Correct answer: A) y = (5/2)x + 5
The intercepts are (0, 5) and (-2, 0). Slope = (0 – 5)/(-2 – 0) = 5/2. So y = (5/2)x + 5.
SAT trap: A negative x-intercept can still produce a positive slope.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
MEDIUM
Question 53
A line contains the points (a, 10) and (a + 4, 22). What is the slope of the line?
A) 2
B) 3
C) 4
D) 12
Show full solution
Correct answer: B) 3
The change in x is (a + 4) – a = 4. The change in y is 22 – 10 = 12. Slope = 12/4 = 3.
SAT trap: The variable a cancels because the horizontal distance is 4.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
MEDIUM
Question 54
Which equation has the same graph as y = 2x – 7?
A) 4x – 2y = 14
B) 4x + 2y = 14
C) 2x – y = -7
D) x – 2y = 7
Show full solution
Correct answer: A) 4x – 2y = 14
From y = 2x – 7, rearrange to 2x – y = 7. Multiplying by 2 gives 4x – 2y = 14.
SAT trap: Equivalent lines can appear in different forms. Simplify before comparing.
FORMS, REPRESENTATIONS, AND EQUIVALENT LINEAR FUNCTIONS
HARD
Question 55
If f(x) = kx + 3 and f(4) – f(1) = 18, what is the value of k?
A) 3
B) 5
C) 6
D) 9
Show full solution
Correct answer: C) 6
f(4) – f(1) = (4k + 3) – (k + 3) = 3k. Set 3k = 18, so k = 6.
SAT trap: The constant cancels in the difference. The change depends on the slope.
What Do Hard SAT Linear Function Questions Look Like?
Harder questions combine function notation, parameter reasoning, equivalent equations, and real-world interpretation. The math is still linear, but the setup is less direct.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 56
A linear function f has f(3) = 2 and f(11) = 18. What is f(0)?
A) -6
B) -4
C) 0
D) 4
Show full solution
Correct answer: B) -4
The slope is (18 – 2)/(11 – 3) = 2. Use f(x) = 2x + b. Since f(3) = 2, b = -4. Therefore f(0) = -4.
SAT trap: For linear functions, f(0) is the y-intercept.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 57
A student's SAT Math practice score is modeled linearly by study hours. At 4 hours, the score is 620. At 12 hours, the score is 700. If the model continues, how many hours correspond to a score of 760?
A) 14
B) 16
C) 18
D) 20
Show full solution
Correct answer: C) 18
The slope is (700 – 620)/(12 – 4) = 10 points per hour. The equation is score = 10h + 580. Set 760 = 10h + 580, so h = 18.
SAT trap: Build the model from two points before answering the target-score question.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 58
For a linear function f with slope 3, f(2a) = f(a) + 12. What is the value of a?
A) 2
B) 3
C) 4
D) 6
Show full solution
Correct answer: C) 4
The input changes from a to 2a, a change of a. With slope 3, the output change is 3a. Since 3a = 12, a = 4.
SAT trap: The y-intercept is not needed because it cancels in a difference.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 59
A linear function f has f(2) = 9 and f(5) = 21. What is f(-1)?
A) -5
B) -3
C) 1
D) 3
Show full solution
Correct answer: B) -3
Slope = (21 – 9)/(5 – 2) = 4. Then f(x) = 4x + b. Using f(2) = 9 gives b = 1. So f(-1) = -4 + 1 = -3.
SAT trap: After finding slope, use one point to find the intercept before extending backward.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 60
Plan A costs $25 plus $0.10 per text message. Plan B costs $10 plus $0.25 per text message. For how many messages do the plans cost the same?
A) 60
B) 80
C) 100
D) 120
Show full solution
Correct answer: C) 100
Set 25 + 0.10n = 10 + 0.25n. Then 15 = 0.15n, so n = 100.
SAT trap: Multiply by 100 to clear decimals if the arithmetic feels messy.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 61
A line has x-intercept 6 and y-intercept 9. What is the value of y when x = 2?
A) 3
B) 6
C) 7
D) 12
Show full solution
Correct answer: B) 6
The intercepts are (6, 0) and (0, 9). Slope = -9/6 = -3/2. The equation is y = (-3/2)x + 9. At x = 2, y = 6.
SAT trap: Intercepts are points. Turn them into a slope and equation before evaluating.
HARD MIXED LINEAR FUNCTION QUESTIONS
MEDIUM
Question 62
A linear function has a slope of 0 and f(-3) = 12. What is f(8)?
A) -3
B) 0
C) 8
D) 12
Show full solution
Correct answer: D) 12
A slope of 0 means the output never changes. Therefore f(8) = 12.
SAT trap: A zero slope is a horizontal line, not a line through the origin.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 63
If f(x) = ax + b and f(x + 3) – f(x) = 18 for all x, what is a?
A) 3
B) 6
C) 9
D) 18
Show full solution
Correct answer: B) 6
f(x + 3) = a(x + 3) + b = ax + 3a + b. Subtracting f(x) = ax + b leaves 3a. Since 3a = 18, a = 6.
SAT trap: The b cancels. The input change of 3 is multiplied by the slope.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 64
A linear function has f(1) = 7, f(3) = 11, and f(5) = 15. What is f(0) + f(6)?
A) 20
B) 22
C) 24
D) 26
Show full solution
Correct answer: B) 22
The slope is (11 – 7)/(3 – 1) = 2. Then f(x) = 2x + 5. So f(0) = 5 and f(6) = 17, giving a sum of 22.
SAT trap: Do not add given table values. Build the function first.
HARD MIXED LINEAR FUNCTION QUESTIONS
HARD
Question 65
A student says that y = 2x + 5 and 2y = 4x + 10 are different lines because the equations look different. Which explanation is correct?
A) They are different because one equation has 2y.
B) They are different because the slopes are different.
C) They are the same line because dividing the second equation by 2 gives y = 2x + 5.
D) They are the same line only when x = 0.
Show full solution
Correct answer: C) They are the same line because dividing the second equation by 2 gives y = 2x + 5.
Divide every term in 2y = 4x + 10 by 2 to get y = 2x + 5. The equations are equivalent and represent the same line.
SAT trap: The SAT often hides equivalent linear functions in different forms.
What Mistakes Cost Students Points on SAT Linear Functions?
| Mistake | Why It Hurts | What to Do Instead |
|---|---|---|
| Using x = 1 as the y-intercept | The y-intercept is where x = 0, not where x = 1. | Find f(0) or set x = 0. |
| Ignoring units | Rates are often dollars per hour, miles per hour, or points per week. | Write what the slope means in words. |
| Mixing up x-intercept and y-intercept | The SAT often gives one and asks for the other. | For x-intercept set y = 0. For y-intercept set x = 0. |
| Not checking for equivalent equations | The same line can be written in many forms. | Simplify to y = mx + b when possible. |
| Skipping the setup in word problems | Random arithmetic can match a tempting wrong answer. | Write the function first, then solve. |
How Should You Study SAT Linear Functions in 2 Weeks?
| Days | Focus | What to Practice |
|---|---|---|
| Days 1-2 | Function notation | Evaluate f(x), work backward from outputs, and read tables. |
| Days 3-5 | Slope and intercepts | Practice slope from two points, x-intercepts, y-intercepts, and equation forms. |
| Days 6-8 | Word problems | Translate fixed costs, repeated rates, and comparison models into functions. |
| Days 9-11 | Equivalent equations | Rearrange standard form, match tables, and compare slopes. |
| Days 12-14 | Timed mixed review | Do 20 mixed linear function questions, review every missed setup, and retest. |
How Did Students Improve on SAT Linear Function Questions?
Case Study 1: Grade 10 student in Fremont, California
This student understood basic equations but missed word problems because she could not tell which number was the starting value and which number was the rate. We rebuilt her approach around two labels: start and change. After ten days of targeted linear model practice, her accuracy on SAT Algebra questions moved from 58% to 84% in timed drills.
Case Study 2: Grade 11 student in Edison, New Jersey
This student was already strong in math but kept losing points on equivalent forms and parameter-based function questions. We trained him to convert every line to y = mx + b unless another form was faster. In three weeks, he stopped missing slope-intercept comparison questions and became more consistent in the harder second module.
Need a Faster SAT Math Score Improvement Plan?
When practice questions are linked to a weekly score strategy, they are most beneficial. Use TestPrepKart’s SAT preparation tools for personalized math practice, error review, live instruction, and mock exams.
Frequently Asked Questions About SAT Linear Functions
Are linear functions important on the SAT?
Yes. The SAT Algebra domain includes linear functions, which can be found in equations, tables, graphs, rates, intercepts, and real-world models. It should be easy for students to switch between all of the representations.
What is the fastest way to solve SAT linear function questions?
First, determine if the inquiry requests an equation, slope, intercept, input, or output. Next, employ the most straightforward representation. The fastest form for many questions is y = mx + b.
How do I know if a table represents a linear function?
The y-values must likewise vary by equal amounts if the x-values rise by similar amounts. A linear relationship is demonstrated by constant first differences.
What is the difference between slope and y-intercept?
Slope is the rate of change, or the amount that y changes when x rises by 1. When x = 0, the y-intercept is the initial value.
Can Desmos help with SAT linear functions?
Yes. Desmos has the ability to graph equations, display intercepts, compare lines, and verify solutions. To know what to enter and how to read the graph, you still need to grasp slope, intercept, and function notation.
How many linear function questions should I practice before the SAT?
60 to 100 mixed linear function questions covering evaluation, slope, intercepts, tables, word problems, and similar equations would be a reasonable goal. Rushing through a lot of simple questions is not as critical as reviewing errors.
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