Find a linear equation to determine the salary Y of the person in year X.

Question

The salary of a person was $45,000 in 2009 and $48,000 in 2011. Find a linear equation to determine the salary Y of the person in year X. Write your equation in (a) as a slope-intercept form.

Answer 1

Let x = time

Let y = salary

 

 

We can set up the information as coordinates on a graph.

 

P₁ = (2009, 45000)

P₂ = (2011, 48000)

 

Lets find the slope of the line using these coordinates.

 

m = (48000 - 45000)/(2011 - 2009)

m = 3000/2

m = 1500

 

Equation is  y = 1500x + b.   We must substitute values from any coordinate to find b.  Let's choose P₁.

 

45000 = 1500(2009)+b

45000 = 3013500+b

-2968500 = b

 

Your equation is

 

y = 1500x - 2968500