The table shows the relationship between the number of players on a team and the minutes each player gets to play.
Players minutes
7 35
8 30
9 25
10 20
Is the relationship a function that ism increasing or decreasing? Is the relationship a function that is linear or nonlinear?
My answer is decreasing and linear.
Agree.
Your answer is incorrect.
The relationship between the number of players on a team and the minutes each player gets to play is not decreasing. The number of players on a team is increasing, but the minutes each player gets to play is decreasing.
However, your answer is correct that the relationship is linear. In a linear function, the rate of change is constant. In this case, as the number of players on the team increases by 1, the minutes each player gets to play decreases by a constant amount.
To determine if the relationship between the number of players on a team and the minutes each player gets to play is increasing or decreasing, you need to examine how the minutes change as the number of players increases.
Looking at the table, you can see that as the number of players increases from 7 to 8, the minutes decrease from 35 to 30. Similarly, as the number of players increases from 8 to 9, the minutes decrease from 30 to 25. This pattern continues when the number of players increases from 9 to 10, and the minutes decrease from 25 to 20.
Since the minutes decrease as the number of players increases, the relationship is indeed decreasing.
Now, let's determine if the relationship is linear or nonlinear. In a linear relationship, the change in one variable (minutes) is constant for a unit change in the other variable (players). To check for linearity, you can calculate the differences in minutes between consecutive data points.
For the given table:
Difference in minutes between 7 and 8 players: 35 - 30 = 5
Difference in minutes between 8 and 9 players: 30 - 25 = 5
Difference in minutes between 9 and 10 players: 25 - 20 = 5
Since the differences in minutes are constant (5) for each unit increase in the number of players, the relationship is linear. Therefore, your answer of decreasing and linear is correct.