Question

In the year 1995, there were 1200 students at pine elementary school. In the year 2010 there were 1500 students. Find the rate of change from 1995 to 2010 and then model the data with linear function. Let x equal the years and y equal the number of students

Answer 1

The rate of change from 1995 to 2010 is 20 students per year and the linear function that models the data will be: $y=20x-38700$

Explanation

In the year 1995, there were 1200 students and in the year 2010, there were 1500 students.

If $x$ represents the year and $y$ represents the number of students, then two points in form of $(x,y)$ will be: $(1995, 1200)$ and $(2010, 1500)$

So, the rate of change or slope = (change in value of y / change in value of x) $=\frac{1500-1200}{2010-1995}= \frac{300}{15}=20$

Now, plugging  slope$(m)$ = 20 and first point $(x_{1}, y_{1}) =(1995,1200)$  into point slope form of linear equation $y-y_{1} =m(x-x_{1})$ , we will get.....

$y-1200=20(x-1995)\\ \\ y-1200=20x-39900\\ \\ y= 20x-39900+1200\\ \\ y= 20x-38700$