Linear Functions Flashcards

The equation y = −4x + 20 represents the remaining battery percentage of a phone x hours after charging stops. When will the battery reach 0%?

Answer: 5 hours

0 = −4x + 20 → 4x = 20 → x = 5.

Two lines are defined by y = 2x + 5 and y = 2x − 3. Which of the following is true?

Answer: They are parallel and never intersect

Both have slope 2 but different y-intercepts (5 and −3), so they are parallel.

A linear function f has the property that f(x + 2) − f(x) = 10 for all x. What is the slope of f?

Answer: 5

f(x+2)−f(x) = m(x+2)+b−(mx+b) = 2m = 10 → m = 5.

The data below models a linear pattern. What is the missing y value? x: 3, 6, 9, 12 | y: 7, 13, 19, ?

Answer: 25

Rate of change = (13−7)/(6−3) = 2; y increases by 6 every 3 units in x; y at x=12 is 19 + 6 = 25.

A caterer charges $200 as a flat fee plus $35 per guest. A client has a budget of $900. What is the maximum number of guests g they can invite?

Answer: 20

200 + 35g ≤ 900 → 35g ≤ 700 → g ≤ 20.

Line t has equation y − 3 = 2(x + 1). What is the y-intercept of line t?

Answer: 5

y − 3 = 2x + 2 → y = 2x + 5; y-intercept = 5.

If the linear function g passes through (0, −7) and (7, 0), what is the slope of g?

Answer: 1

Slope = (0 − (−7))/(7 − 0) = 7/7 = 1.

An electrician charges $90 for the first hour and $60 for each subsequent hour. After h hours total (h ≥ 1), which function gives the total bill B?

Answer: B(h) = 60h + 30

B = 90 + 60(h−1) = 90 + 60h − 60 = 60h + 30.