Bluebook SAT Test Linear Functions 8 — Questions and Answers
Question 1: Two lines are defined by y = 4x − 3 and y = (1/4)x + 2. Which statement about these lines is true?
- They are parallel
- They intersect at exactly one point (Correct answer)
- They are perpendicular
- They are the same line
Correct answer: They intersect at exactly one point
The slopes 4 and 1/4 are different (product = 1, not −1), so the lines are not perpendicular and not parallel — they intersect at exactly one point.
Question 2: The function f(x) = −2x + 10 is defined for 0 ≤ x ≤ 5. What is the range of f?
- 0 ≤ f(x) ≤ 5
- 0 ≤ f(x) ≤ 10 (Correct answer)
- 5 ≤ f(x) ≤ 10
- −10 ≤ f(x) ≤ 10
Correct answer: 0 ≤ f(x) ≤ 10
At x = 0: f = 10; at x = 5: f = 0; since slope is negative, f decreases, so range is 0 ≤ f(x) ≤ 10.
Question 3: The equation of a line is y = 5 − (3/2)x. What is the slope of a line perpendicular to this line?
- 3/2
- −3/2
- 2/3 (Correct answer)
- −2/3
Correct answer: 2/3
The slope of the given line is −3/2; the perpendicular slope is the negative reciprocal: 2/3.
Question 4: A salesperson earns a base salary of $2,000 per month plus a 5% commission on all sales. If the salesperson earns $2,750 in a month, what were their total sales that month?
- $13,750
- $15,000 (Correct answer)
- $15,500
- $17,500
Correct answer: $15,000
2000 + 0.05s = 2750 → 0.05s = 750 → s = $15,000.
Question 5: In the function f(x) = 6x + b, if the graph passes through (−2, 4), what is the value of b?
- 8
- 12
- 16 (Correct answer)
- −8
Correct answer: 16
4 = 6(−2) + b → 4 = −12 + b → b = 16.
Question 6: A school's enrollment has been declining linearly. In 2020 the school had 840 students, and in 2024 it has 680 students. If this trend continues, in what year will enrollment reach 560 students?
- 2026
- 2027 (Correct answer)
- 2028
- 2029
Correct answer: 2027
Rate = (680 − 840)/4 = −40 students/yr; from 2024: 680 − 40t = 560 → 40t = 120 → t = 3 more years → 2027.
Question 7: A linear function g satisfies g(2) = 7 and the slope is −4. What is g(5)?
- −5 (Correct answer)
- −4
- −3
- −2
Correct answer: −5
g(x) = −4x + b; 7 = −4(2) + b → b = 15; g(5) = −4(5) + 15 = −20 + 15 = −5.
Bluebook SAT Test Linear Functions 8
Two lines are defined by y = 4x − 3 and y = (1/4)x + 2.
Which statement about these lines is true?