Option A:
The equation for the trend line is y = 82x + 998.
Solution:
The points on the line are (2, 1162) and (11, 1900).
Here, [tex]x_1=2, y_1=1162, x_2 = 11, y_2=1900[/tex]
Slope of the line:
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
[tex]$m=\frac{1900-1162}{11-2}[/tex]
[tex]$m=\frac{738}{9}[/tex]
m = 82
Point-slope formula:
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex]
[tex]y-1162=82\left(x-2\right)[/tex]
[tex]y-1162=82x-164[/tex]
Add 1162 on both sides of the equation.
[tex]y=82x+998[/tex]
The equation for the trend line is y = 82x + 998.
Hence Option A is the correct answer.
