Exercise 50 Page 194

Let's first calculate the rate of the student body growth at Jefferson High School. Then we will use this information to find how many students Fairview High School had in $2006.$

Rate of the Student Body Growth at Jefferson High School

It is given that in $2000$ there were $1125$ students at the school. By $2006,$ the student body had increased to $1425$ students. Let the $x\text{-}$coordinate represent the year and the $y\text{-}$coordinate represent the number of students. Then, we can write the following ordered pairs. Let's substitute these into the Slope Formula and calculate the rate of student body growth. This means the number of students at Jefferson High School is growing by $50$ students every year.

The Number of Students at Fairview High School

We know that the student body of Fairview High School grows at the same rate as Jefferson High School. Therefore, its slope is $50.$ Also, we are told that in $2001$ the school had $1275$ students. This allows us to write the ordered pair $(2001,1275).$ Let the number of students in $2006$ be $x,$ so the second ordered pair is $(2006,x).$ Let's substitute these ordered pairs and the value of the slope into the Slope Formula. We got the equation for the unknown $x.$ Let's solve it! Therefore, the number of students at Fairview High School in $2006$ was $1525$ students.