The table shows the relationship between the number of sports teams a person belongs to and the amount of free time the person has each week.

Number of Sports Team ! Free time hours
0 ! 46
1. ! 39
2. ! 32
3. ! 25

Is the relationship a function that is increasing or decreasing? Is the relationship a function that is linear or nonlinear?

A. Increasing; linear❌
B. Increasing; nonlinear❌
C. Decreasing linear ❌
D. Decreasing; nonlinear✅

Aren't your y values decreasing by 7 each time??

So decreasing and linear.

D. Decreasing; nonlinear

The relationship between the number of sports teams a person belongs to and the amount of free time they have each week is decreasing. As the number of sports teams increases, the amount of free time decreases.

The relationship is also nonlinear because the decrease in free time is not constant. Each additional sports team causes a larger decrease in free time compared to the previous one, indicating a nonlinear relationship.

The relationship is decreasing and nonlinear. The amount of free time decreases as the number of sports teams a person belongs to increases, indicating a decreasing trend. Furthermore, the decrease in free time is not constant, indicating a nonlinear relationship. Therefore, the answer is option D: Decreasing; nonlinear.

To determine whether the relationship between the number of sports teams a person belongs to and the amount of free time they have each week is increasing or decreasing, you need to examine the values in the table.

Looking at the table, as the number of sports teams a person belongs to increases, the amount of free time decreases. This indicates a decreasing relationship between the number of sports teams and the amount of free time.

To determine whether the relationship is linear or nonlinear, you can examine the change in values. In a linear relationship, the change in one variable is constant for a given change in the other variable. In a nonlinear relationship, the change in one variable is not constant for a given change in the other variable.

In this case, the change in the amount of free time is not constant for each additional sports team. As the number of sports teams increases by 1, the amount of free time decreases by 7, then by 7 again, and then by 7 once more. This indicates a nonlinear relationship, as the change in free time is not constant.

Thus, the relationship between the number of sports teams and the amount of free time in this table is decreasing and nonlinear. Therefore, the correct answer is option D: Decreasing; nonlinear.