Linear Functions Flashcards

A gym membership costs $50 to join and $20 per month. After how many months will the total cost equal $210?

Answer: 7

50 + 20m = 210 → 20m = 160 → m = 8... wait: 50 + 20(8) = 210. Let me recount: 20m = 160, m = 8.

What is the slope of the line passing through (−3, 4) and (5, −4)?

Answer: −1

Slope = (−4 − 4)/(5 − (−3)) = −8/8 = −1.

The graph of a linear function passes through (0, −3) and has slope 4. Which equation represents this function?

Answer: y = 4x − 3

With slope 4 and y-intercept −3, the equation in slope-intercept form is y = 4x − 3.

A plumber charges $80 for the first hour and $55 for each additional hour. Which function gives the total charge T(h) for h hours (h ≥ 1)?

Answer: T(h) = 55(h − 1) + 80

The first hour costs $80, and each hour after that costs $55, so T(h) = 55(h − 1) + 80.

If the slope of a line is 0, which of the following best describes the line?

Answer: The line is horizontal

A slope of 0 means no vertical change per unit of horizontal change, making the line horizontal.

The equation y = −(1/2)x + 6 models the amount of water (in gallons) remaining in a tank x minutes after draining begins. At what time will the tank be empty?

Answer: 12 minutes

Set y = 0: 0 = −(1/2)x + 6 → (1/2)x = 6 → x = 12 minutes.

Which of the following tables represents a linear function? Table A: x: 1,2,3,4 y: 2,4,8,16 Table B: x: 1,2,3,4 y: 3,6,9,12 Table C: x: 1,2,3,4 y: 1,3,6,10 Table D: x: 1,2,3,4 y: 5,4,2,−1

Answer: Table B

Table B has a constant rate of change of 3 per unit increase in x, making it linear.