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 4 minutes of play, the game awards one-half point, and for every 10 minutes of play, the game awards one and one-fourth points.
Part A: Find the constant of proportionality. Show every step of your work. (4 points)
Part B: Write an equation that represents the relationship. Show every step of your work.
Part A:
Let x be the amount of time (in minutes) played and y be the number of points awarded.
From the given information, we can set up the following proportion:
(4 minutes / 0.5 point) = (10 minutes / 1.25 points)
Cross-multiplying, we get:
4 minutes * 1.25 points = 0.5 point * 10 minutes
5 minutes * points = 5 minutes * points
Therefore, we can conclude that the constant of proportionality is 1.25.
Part B:
Using the information from Part A, we know that the equation representing the relationship is y = 1.25x.
This equation states that the number of points awarded (y) is equal to 1.25 times the amount of time played (x).