Answer:
[tex]y = 0.045x -0.445[/tex]
Step-by-step explanation:
Given
[tex](x_1,y_1)=(11,5\%)[/tex] ---- in 2011
[tex](x_2,y_2)=(15,23\%)[/tex] --- in 2015
Required
Linear equation for x years after 2000
First, calculate the slope
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{23\% - 5\%}{15 - 11}[/tex]
[tex]m = \frac{18\%}{4}[/tex]
[tex]m = 4.5\%[/tex]
[tex]m = 0.045[/tex]
The equation for x years after 2000 is:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 0.045(x - 11) + 5\%[/tex]
[tex]y = 0.045x - 0.495 + 0.05[/tex]
[tex]y = 0.045x -0.445[/tex]
