Linear Functions Flashcards

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?

Answer: 5h + 8 ≤ 33

Total cost = 5h + 8; for at most $33: 5h + 8 ≤ 33.

What is the y-intercept of the line defined by the equation 2y − 6x = 10?

Answer: 5

Divide by 2: y = 3x + 5, so the y-intercept is 5.

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?

Answer: L(t) = 12t + 8

She starts with 8 (y-intercept) and produces 12 per hour (slope): L(t) = 12t + 8.

A line passes through (a, 3) and (7, 9), and has a slope of 2. What is the value of a?

Answer: 4

Slope = (9 − 3)/(7 − a) = 2 → 6 = 2(7 − a) → 6 = 14 − 2a → 2a = 8 → a = 4.

Which of the following is the graph of a function with a negative slope and a positive y-intercept?

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.

If the linear function f(x) = (3/4)x − 2, what is f(8)?

Answer: 4

f(8) = (3/4)(8) − 2 = 6 − 2 = 4.

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?

Answer: 20th day

Set W = 0: 0 = −1.5d + 30 → 1.5d = 30 → d = 20 days.