FOCUSED PRACTICE

SAT slope and linear models practice

Connect a table or a word problem to a line. Keep rate, starting value, and units separate.

The idea to remember

In y = mx + b, m is the change in y for each one-unit increase in x, and b is the value when x is zero.

A worked example

A table contains (2, 11) and (5, 23). The slope is (23 - 11)/(5 - 2) = 4. Substitute either point to find b = 3. The model is y = 4x + 3.

A common trap

The first y-value in a table is not the intercept unless its x-value is zero.

For a longer walkthrough, read Read SAT tables, slopes, and growth models with confidence.

By Graph Math Practice editorial team · Reviewed 2026-09-05

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32 original exercises. Each topic has 8. Short sets sample available questions without repeats within a session. No time limit.

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All 8 questions, with explanations

Work on paper or read at your own pace. Open each explanation after choosing an answer. These are the same original questions used in the interactive tool.

1. A linear function has values f(1) = 10 and f(4) = 19. What is its slope?
1. 3
2. 4
3. 9
4. 7
Show answer and explanation
Answer: A. 3
Slope is change in output divided by change in input: (19 - 10)/(4 - 1) = 9/3 = 3. The output rises 3 units for each one-unit increase in input.
2. A rental service charges a fixed fee plus $3 per hour. A 4-hour rental costs $19. What is the fixed fee, in dollars?
1. 19
2. 3
3. 31
4. 7
Show answer and explanation
Answer: D. 7
The hourly part costs 3 × 4 = 12. Subtract it from the total: 19 - 12 = 7. In C = 3h + 7, the fixed fee is the vertical intercept.
3. A linear function has values f(2) = 16 and f(5) = 28. What is its slope?
1. 12
2. 8
3. 4
4. 5
Show answer and explanation
Answer: C. 4
Slope is change in output divided by change in input: (28 - 16)/(5 - 2) = 12/3 = 4. The output rises 4 units for each one-unit increase in input.
4. A rental service charges a fixed fee plus $4 per hour. A 5-hour rental costs $28. What is the fixed fee, in dollars?
1. 48
2. 8
3. 28
4. 4
Show answer and explanation
Answer: B. 8
The hourly part costs 4 × 5 = 20. Subtract it from the total: 28 - 20 = 8. In C = 4h + 8, the fixed fee is the vertical intercept.
5. A linear function has values f(3) = 24 and f(6) = 39. What is its slope?
1. 5
2. 6
3. 15
4. 9
Show answer and explanation
Answer: A. 5
Slope is change in output divided by change in input: (39 - 24)/(6 - 3) = 15/3 = 5. The output rises 5 units for each one-unit increase in input.
6. A rental service charges a fixed fee plus $5 per hour. A 6-hour rental costs $39. What is the fixed fee, in dollars?
1. 39
2. 5
3. 69
4. 9
Show answer and explanation
Answer: D. 9
The hourly part costs 5 × 6 = 30. Subtract it from the total: 39 - 30 = 9. In C = 5h + 9, the fixed fee is the vertical intercept.
7. A linear function has values f(4) = 34 and f(7) = 52. What is its slope?
1. 18
2. 10
3. 6
4. 7
Show answer and explanation
Answer: C. 6
Slope is change in output divided by change in input: (52 - 34)/(7 - 4) = 18/3 = 6. The output rises 6 units for each one-unit increase in input.
8. A rental service charges a fixed fee plus $6 per hour. A 7-hour rental costs $52. What is the fixed fee, in dollars?
1. 94
2. 10
3. 52
4. 6
Show answer and explanation
Answer: B. 10
The hourly part costs 6 × 7 = 42. Subtract it from the total: 52 - 42 = 10. In C = 6h + 10, the fixed fee is the vertical intercept.

Scope reference: College Board’s section overview. Questions are independently authored and are not official exam material.

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