Bluebook SAT Test Linear Functions 7 — Questions and Answers
Question 1: The cost of renting a bicycle is $5 per hour plus an additional one-time $8 fee. Which inequality represents the number of hours h for which the total cost is at most $33?
- 5h + 8 ≤ 33 (Correct answer)
- 5h − 8 ≤ 33
- 8h + 5 ≤ 33
- 5h + 8 ≥ 33
Correct answer: 5h + 8 ≤ 33
Total cost = 5h + 8; for at most $33: 5h + 8 ≤ 33.
Question 2: What is the y-intercept of the line defined by the equation 2y − 6x = 10?
- 3
- 5 (Correct answer)
- 10
- −5
Correct answer: 5
Divide by 2: y = 3x + 5, so the y-intercept is 5.
Question 3: A baker makes 12 loaves of bread per hour. She already has 8 loaves ready when the bakery opens. Which function gives the total number of loaves L(t) available after t hours of baking?
- L(t) = 8t + 12
- L(t) = 12t − 8
- L(t) = 12t + 8 (Correct answer)
- L(t) = 8t − 12
Correct answer: L(t) = 12t + 8
She starts with 8 (y-intercept) and produces 12 per hour (slope): L(t) = 12t + 8.
Question 4: A line passes through (a, 3) and (7, 9), and has a slope of 2. What is the value of a?
- 2
- 3
- 4 (Correct answer)
- 5
Correct answer: 4
Slope = (9 − 3)/(7 − a) = 2 → 6 = 2(7 − a) → 6 = 14 − 2a → 2a = 8 → a = 4.
Question 5: Which of the following is the graph of a function with a negative slope and a positive y-intercept?
- A line rising from left to right crossing the positive y-axis
- A line falling from left to right crossing the positive y-axis (Correct answer)
- A line rising from left to right crossing the negative y-axis
- A line falling from left to right crossing the negative y-axis
Correct answer: A line falling from left to right crossing the positive y-axis
Negative slope means the line falls left to right; positive y-intercept means it crosses the y-axis above the origin.
Question 6: If the linear function f(x) = (3/4)x − 2, what is f(8)?
- 2
- 4 (Correct answer)
- 6
- 8
Correct answer: 4
f(8) = (3/4)(8) − 2 = 6 − 2 = 4.
Question 7: The linear function W(d) = −1.5d + 30 models the amount of dog food (in cups) remaining in a bag after d days. On what day will the bag be empty?
- 15th day
- 18th day
- 20th day (Correct answer)
- 25th day
Correct answer: 20th day
Set W = 0: 0 = −1.5d + 30 → 1.5d = 30 → d = 20 days.
Bluebook SAT Test Linear Functions 7
The cost of renting a bicycle is $5 per hour plus an additional one-time $8 fee.
Which inequality represents the number of hours h for which the total cost is at most $33?