Bluebook SAT Test Linear Functions 4 — Questions and Answers
Question 1: The linear function h models the height (in feet) of a balloon t minutes after launch: h(t) = 120 + 15t. What is the height of the balloon after 8 minutes?
- 135 feet
- 180 feet
- 195 feet
- 240 feet (Correct answer)
Correct answer: 240 feet
h(8) = 120 + 15(8) = 120 + 120 = 240 feet.
Question 2: What is the x-intercept of the line with equation 3x + 5y = 15?
- (3, 0)
- (5, 0) (Correct answer)
- (0, 3)
- (15, 0)
Correct answer: (5, 0)
Set y = 0: 3x = 15 → x = 5, so the x-intercept is (5, 0).
Question 3: Two linear functions are defined as f(x) = 2x + 3 and g(x) = 2x − 5. Which of the following is true about their graphs?
- They intersect at one point
- They are the same line
- They are parallel (never intersect) (Correct answer)
- They are perpendicular
Correct answer: They are parallel (never intersect)
Both functions have slope 2 but different y-intercepts, so their graphs are parallel lines that never intersect.
Question 4: A student earns $12.50 per hour working part-time. If the student works h hours and has already saved $75, which function gives the total savings S(h)?
- S(h) = 75h + 12.50
- S(h) = 12.50h − 75
- S(h) = 12.50 + 75h
- S(h) = 12.50h + 75 (Correct answer)
Correct answer: S(h) = 12.50h + 75
The initial savings ($75) is the y-intercept and the hourly rate ($12.50) is the slope: S(h) = 12.50h + 75.
Question 5: Line m has the equation x = −4. Which of the following best describes this line?
- A line with slope −4
- A horizontal line at y = −4
- A vertical line at x = −4 (Correct answer)
- A line with y-intercept −4
Correct answer: A vertical line at x = −4
Equations of the form x = k represent vertical lines passing through (k, 0) on the x-axis.
Question 6: If g(x) = mx + 4 and g(5) = 19, what is the value of m?
- 2
- 3 (Correct answer)
- 4
- 5
Correct answer: 3
19 = m(5) + 4 → 5m = 15 → m = 3.
Question 7: The table shows a linear relationship between x and y. x: −2 0 2 4 y: 1 5 9 13 Which equation represents this relationship?
- y = 4x + 5
- y = 2x + 5 (Correct answer)
- y = 3x + 5
- y = 2x + 1
Correct answer: y = 2x + 5
From the table, slope = (9 − 5)/(2 − 0) = 2 and y-intercept = 5, giving y = 2x + 5.
Bluebook SAT Test Linear Functions 4
The linear function h models the height (in feet) of a balloon t minutes after launch: h(t) = 120 + 15t.
What is the height of the balloon after 8 minutes?