Linear Functions Flashcards

The line 2y = 6x − 10 is graphed. What are the slope and y-intercept?

Answer: slope = 3, y-intercept = −5

Divide by 2: y = 3x − 5; slope = 3, y-intercept = −5.

A linear function has the values shown: f(−2) = 8 and f(4) = −4. What is f(1)?

Answer: 2

Slope = (−4 − 8)/(4 − (−2)) = −12/6 = −2; f(x) = −2x + b; f(−2) = 8 → b = 4; f(1) = −2 + 4 = 2.

A parking garage charges $4.00 for the first hour and $2.50 for each additional hour. Which function gives the total charge T for h hours (h ≥ 1)?

Answer: T(h) = 2.50(h − 1) + 4.00

For h ≥ 1, the cost is $4.00 for hour 1 plus $2.50 for each of the remaining (h − 1) hours: T = 2.50(h − 1) + 4.00.

If the graph of y = kx − 6 passes through (3, 0), what is the value of k?

Answer: 2

0 = k(3) − 6 → 3k = 6 → k = 2.

Lines p and q are perpendicular. Line p has slope −5/2. What is the slope of line q?

Answer: 2/5

The perpendicular slope is the negative reciprocal: −1/(−5/2) = 2/5.

A linear function f has f(2) = 9 and f(5) = 18. What is f(0)?

Answer: 3

Slope = (18 − 9)/(5 − 2) = 3; f(2) = 9 → 9 = 3(2) + b → b = 3; f(0) = 3.

The equation 5x − y = 12 can be rewritten as which of the following?

Answer: y = 5x − 12

Subtract 5x from both sides and multiply by −1: y = 5x − 12.

A store earns $8 profit per item sold. After selling 25 items, the total profit is $50 (because it first paid a $150 setup cost). Which function P(n) models total profit after n items?

Answer: P(n) = 8n − 150

Verify: P(25) = 8(25) − 150 = 200 − 150 = 50 ✓; the setup cost is a fixed negative y-intercept.