Answer:
It can not be modeled by a linear function
Step-by-step explanation:
The given parameters can be represented as:
![(x_1,y_1) = (1,64)](https://tex.z-dn.net/?f=%28x_1%2Cy_1%29%20%3D%20%281%2C64%29)
![(x_2,y_2) = (2,32)](https://tex.z-dn.net/?f=%28x_2%2Cy_2%29%20%3D%20%282%2C32%29)
![(x_3,y_3) = (3,16)](https://tex.z-dn.net/?f=%28x_3%2Cy_3%29%20%3D%20%283%2C16%29)
Where: x = rounds and y = players
Required:
Determine if it can be represented by a linear function
To do this, we simply calculate the slope (m)
![m = \frac{y_2 - y_1}{x_2 - x_1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_2%20-%20y_1%7D%7Bx_2%20-%20x_1%7D)
and
![m = \frac{y_3 - y_2}{x_3 - x_2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7By_3%20-%20y_2%7D%7Bx_3%20-%20x_2%7D)
Using:
, we have:
![m = \frac{32 - 64}{2 - 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B32%20-%2064%7D%7B2%20-%201%7D)
![m = \frac{-32}{ 1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-32%7D%7B%201%7D)
![m = -32](https://tex.z-dn.net/?f=m%20%3D%20-32)
Using
, we have:
![m = \frac{16 - 32}{3 - 2}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B16%20-%2032%7D%7B3%20-%202%7D)
![m = \frac{-16}{1}](https://tex.z-dn.net/?f=m%20%3D%20%5Cfrac%7B-16%7D%7B1%7D)
![m = -16](https://tex.z-dn.net/?f=m%20%3D%20-16)
<em>Since both slopes are not the same, the relationship be modeled by a linear function</em>