Question

Determine the constant rate of change (slope) of the linear function. A high school basketball team notices that attendance at its games changes at a constant rate based on the number of losses the team has suffered. When the team had lost eight games, 265 people attended the next game. When the team had lost 15 games, 153 people attended the next game. people attending per loss suffered Explain what it means in this context. The change in the per game is times as great as the change in the number of .

Answer 1

The change in the people attending per game is 14.7 times as great as the change in the number of lost games.

This mean every game is lost, 14.7 less people (as the slope is negative) attend the next game.

Explanation:

To calculate the slope, we need to relate two points of the function.

The slope
`m` of the function
`y=m*x+b` can be calculated as

We have the point (x=8, y=256) when it says 265 people attended the next game after the team lost 8 games.

The second point is (x=15, y=153) when it says 153 people attended the next game after the team lost 15 games.

We can write

`y_2-y_1=(m*x_2+b)-(m*x_1+b)=m*(x_2-x_1)\\\\m=(y_2-y_1)/(x_2-x_1) =(256-153)/(8-15)=(103)/(-7)=  -14.7`