The rate of change from 1995 to 2010 is 20 students per year and the linear function that models the data will be: [tex]y=20x-38700[/tex]
Explanation
In the year 1995, there were 1200 students and in the year 2010, there were 1500 students.
If [tex]x[/tex] represents the year and [tex]y[/tex] represents the number of students, then two points in form of [tex](x,y)[/tex] will be: [tex](1995, 1200)[/tex] and [tex](2010, 1500)[/tex]
So, the rate of change or slope = (change in value of y / change in value of x) [tex]=\frac{1500-1200}{2010-1995}= \frac{300}{15}=20[/tex]
Now, plugging slope[tex](m)[/tex] = 20 and first point [tex](x_{1}, y_{1}) =(1995,1200)[/tex] into point slope form of linear equation [tex]y-y_{1} =m(x-x_{1})[/tex] , we will get.....
[tex]y-1200=20(x-1995)\\ \\ y-1200=20x-39900\\ \\ y= 20x-39900+1200\\ \\ y= 20x-38700[/tex]
