Question

For a certain video game, the number of points awarded to the player is proportional to the amount of time the game is played. For every 1 minute of play, the game awards one-half point, and for every 5 minutes of play, the game awards two and one-half points.

Part A: Find the constant of proportionality. Show every step of your work.

Part B: Write an equation that represents the relationship. Show every step of your work.

Part C: Describe how you would graph the relationship. Use complete sentences.

Part D: How many points are awarded for 18 minutes of play?

Answer 1

A. 0.5 points/minute

B. y = (0.5 points/min)*x

C. x axis: 0 - 60 minutes, y axis: 0 - 30 points.

D. 9 points

Explanation:

Part A: Find the constant of proportionality. In this example, the constant of proportionality is the points scored per time unit played. We are told that 1 minute of play adds (1/2) point to the score. So the constant is 0.5 points/minute.

Part B: Write an equation that represents the relationship. Show every step of your work. Let y be the total points and x the time played, in minutes. The equation would be:

y = 0.5(points/minute)*x

For x = 5 minutes, y is 2.5 points.

Part C: Describe how you would graph the relationship. Use complete sentences.

The x axis is marked in minutes and the y axis is points. A reasonable range would be 0 - 60 minutes, which could produce up to 30 points.

Part D: How many points are awarded for 18 minutes of play?

y = (0.5 points/minute)*x

y = (0.5 points/minute)*(18 minutes)

y = 9 points