Answer: A) ![(0,900)\ and\ (3,1500)](https://tex.z-dn.net/?f=%280%2C900%29%5C%20and%5C%20%283%2C1500%29)
B) Slope=200, It means enrollment of 200 students increases each year.
C) ![P=200t+900](https://tex.z-dn.net/?f=P%3D200t%2B900)
D) 2500 students.
Step-by-step explanation:
Given: The student enrollment of the high school, P, has increased at a constant rate each year, t, since 2009.
At 2009, t=0 and at 2012, t=3 [Since 2012-2009=3 years]
A) In points , the given enrollment numbers will be written as:-
![(0,900)\ and\ (3,1500)](https://tex.z-dn.net/?f=%280%2C900%29%5C%20and%5C%20%283%2C1500%29)
B) The slope of the line passing through
is given by:-
![m=\frac{y_2-y_1}{x_2-x_1}=\frac{1500-900}{3-0}=\frac{600}{3}=200](https://tex.z-dn.net/?f=m%3D%5Cfrac%7By_2-y_1%7D%7Bx_2-x_1%7D%3D%5Cfrac%7B1500-900%7D%7B3-0%7D%3D%5Cfrac%7B600%7D%7B3%7D%3D200)
It means enrollment of 200 students increases each year.
C) The linear equation with slope= 200 and and the initial number of students (900) is given by
![P=200t+900](https://tex.z-dn.net/?f=P%3D200t%2B900)
D) At 2017, t=8 [Since 2017-2009=8]
Then ![P=200(8)+900=1600+900=2500](https://tex.z-dn.net/?f=P%3D200%288%29%2B900%3D1600%2B900%3D2500)
The high school's enrollment in 2017 = 2500 students.