Question

the given table shows the participation in the town soccer league during its first five seasons. town recreational soccer league participation year number of participants 1 88 2 95 3 100 4 108 5 115 which is the equation of the trend line that can be generated by using the data from years 1 and 5? ( y = 6.75x + 81.25 ) ( y = 6.75x - 1.75 ) ( y = 6.75x + 148.75 ) ( y = 6.75x - 688.25 )

Explanation:

Step1: Find the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\).
For year \(1\) (\(x_1 = 1,y_1=88\)) and year \(5\) (\(x_2 = 5,y_2 = 115\)).
\(m=\frac{115 - 88}{5 - 1}=\frac{27}{4}=6.75\).

Step2: Find the y - intercept

Use the point - slope form \(y - y_1=m(x - x_1)\).
Substitute \(m = 6.75,x_1 = 1,y_1=88\).
\(y-88=6.75(x - 1)\).
Expand: \(y-88=6.75x-6.75\).
Solve for \(y\): \(y=6.75x-6.75 + 88\).
\(y=6.75x+81.25\).

Answer:

\(y = 6.75x + 81.25\)