Bluebook SAT Test Linear Functions 1 — Questions and Answers
Question 1: A line passes through the points (2, 5) and (6, 13). What is the slope of the line?
- 1
- 2 (Correct answer)
- 3
- 4
Correct answer: 2
Slope = (13 − 5)/(6 − 2) = 8/4 = 2.
Question 2: The function f(x) = 3x − 7 gives the profit (in dollars) a vendor earns when selling x items. What does the value 3 represent in this context?
- The fixed cost per day
- The profit per item sold (Correct answer)
- The total number of items
- The break-even point
Correct answer: The profit per item sold
In f(x) = mx + b, the slope m = 3 is the rate of change, i.e., the profit earned per each additional item sold.
Question 3: Which equation represents a line with a slope of −2 and a y-intercept of 5?
- y = 5x − 2
- y = 2x + 5
- y = −2x + 5 (Correct answer)
- y = −2x − 5
Correct answer: y = −2x + 5
Slope-intercept form is y = mx + b where m = −2 and b = 5, giving y = −2x + 5.
Question 4: A car rental company charges a flat fee of $30 plus $0.25 per mile driven. Which function models the total cost C(m) for m miles?
- C(m) = 0.30m + 25
- C(m) = 30m + 0.25
- C(m) = 0.25m + 30 (Correct answer)
- C(m) = 25m + 0.30
Correct answer: C(m) = 0.25m + 30
The flat fee is the y-intercept (30) and the per-mile rate is the slope (0.25), so C(m) = 0.25m + 30.
Question 5: If f(x) = −4x + 11, what is the value of f(3)?
- −1 (Correct answer)
- 1
- 23
- −1
Correct answer: −1
f(3) = −4(3) + 11 = −12 + 11 = −1.
Question 6: The table below shows values for a linear function g(x). x: 0 1 2 3 g: 7 10 13 16 What is the value of g(10)?
- 34
- 37 (Correct answer)
- 40
- 43
Correct answer: 37
The slope is 3 and the y-intercept is 7, so g(x) = 3x + 7; g(10) = 30 + 7 = 37.
Question 7: Line ℓ has the equation 4x − 2y = 10. What is the x-intercept of line ℓ?
- (5/2, 0) (Correct answer)
- (0, −5)
- (2, 0)
- (−5, 0)
Correct answer: (5/2, 0)
Set y = 0: 4x = 10 → x = 5/2, so the x-intercept is (5/2, 0).
Bluebook SAT Test Linear Functions 1
A line passes through the points (2, 5) and (6, 13).
What is the slope of the line?