Bluebook SAT Test Linear Functions 5 — Questions and Answers
Question 1: A truck travels at a constant speed. After 2 hours it has traveled 110 miles, and after 5 hours it has traveled 275 miles. How many miles per hour is the truck traveling?
- 50 mph
- 55 mph (Correct answer)
- 60 mph
- 65 mph
Correct answer: 55 mph
Rate = (275 − 110)/(5 − 2) = 165/3 = 55 mph.
Question 2: Which line is perpendicular to y = (2/3)x + 1?
- y = (2/3)x − 4
- y = (3/2)x + 1
- y = −(3/2)x + 5 (Correct answer)
- y = −(2/3)x + 1
Correct answer: y = −(3/2)x + 5
Perpendicular slopes are negative reciprocals; the negative reciprocal of 2/3 is −3/2, giving y = −(3/2)x + 5.
Question 3: A linear function f satisfies f(0) = −6 and f(4) = 10. What is f(6)?
- 16
- 18 (Correct answer)
- 20
- 24
Correct answer: 18
Slope = (10 − (−6))/(4 − 0) = 16/4 = 4; f(x) = 4x − 6; f(6) = 24 − 6 = 18.
Question 4: In the function P(t) = 1200 − 40t, P represents the number of gallons of water in a pool and t represents time in hours. What does −40 represent?
- The initial amount of water in the pool
- The time it takes to empty the pool
- The rate at which water drains (40 gallons per hour) (Correct answer)
- The total gallons drained
Correct answer: The rate at which water drains (40 gallons per hour)
The coefficient of t (slope) = −40 represents the rate of change: water decreases by 40 gallons each hour.
Question 5: If the equation of a line is written as 6x − 2y = 8, what is the slope of the line?
- 3 (Correct answer)
- −3
- 4
- −4
Correct answer: 3
Rewrite in slope-intercept form: −2y = −6x + 8 → y = 3x − 4, so the slope is 3.
Question 6: The function C(x) = 0.08x + 15 represents the monthly cost (in dollars) of a streaming service, where x is the number of premium channels added. If a customer pays $23.40, how many premium channels did they add?
- 99
- 101
- 105 (Correct answer)
- 115
Correct answer: 105
0.08x + 15 = 23.40 → 0.08x = 8.40 → x = 105.
Question 7: A line ℓ has slope −3 and passes through (2, 7). Which point also lies on line ℓ?
- (3, 4)
- (4, 1)
- (0, 13) (Correct answer)
- (1, 10)
Correct answer: (0, 13)
Equation: y − 7 = −3(x − 2) → y = −3x + 13; at x = 0, y = 13. Checking (0, 13): 13 = −3(0) + 13 ✓.
Bluebook SAT Test Linear Functions 5
A truck travels at a constant speed.
After 2 hours it has traveled 110 miles, and after 5 hours it has traveled 275 miles.
How many miles per hour is the truck traveling?