A basketball player makes an average of 10 points for every 15 shots taken. Each shot made by the player is a 2-point shot. The variables in this situation are the number of 2-point shots taken and the number of points made.
What is the rate of change for this situation? Express your answer as a fraction.
To find the rate of change in this situation, we need to determine how the number of points made (y) changes with respect to the number of 2-point shots taken (x).
Given that the player makes an average of 10 points for every 15 shots taken, we can express this relationship as a ratio:
(y points) / (x shots) = 10 points / 15 shots
To simplify this ratio, we can reduce it by dividing both the numerator and denominator by 5:
(y points) / (x shots) = 2 points / 3 shots
From this ratio, we can see that for every 3 shots taken, the player makes 2 points. Therefore, the rate of change is 2 points for every 3 shots taken.
Expressing this rate of change as a fraction, we can write it as:
2/3