Question

the table below shows the participation in the town soccer league during its first five seasons.
town recreational soccer league participation

year	number of participants
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?
○ $y = 6.75x - 688.25$
○ $y = 6.75x - 1.75$
○ $y = 6.75x + 81.25$
○ $y = 6.75x + 148.75$

Explanation:

Step1: Identify two data points

The points are $(x_1,y_1)=(1,88)$ and $(x_2,y_2)=(5,115)$

Step2: Calculate slope $m$

$m=\frac{y_2-y_1}{x_2-x_1}=\frac{115-88}{5-1}=\frac{27}{4}=6.75$

Step3: Find y-intercept $b$

Use $y=mx+b$ with $(1,88)$:
$88=6.75(1)+b$
$b=88-6.75=81.25$

Step4: Form trend line equation

$y=6.75x+81.25$

Answer:

$y=6.75x+81.25$ (the third option)