Answer:
[tex]y = \$335931.5 + \$110668.5x[/tex]
Step-by-step explanation:
Given
[tex]Salary\ in\ 2000 = \$446,600[/tex] (Median)
[tex]Salary\ in\ 2008 = \$1,331,948[/tex] (Median)
Required
Determine a Linear Equation
The above question illustrates an Arithmetic Progression (AP)
The nth term of an AP is
[tex]T_n = a + (n - 1) d[/tex]
In this case;
[tex]a = Salary\ in\ 2000 = \$446,600[/tex]
[tex]n = 2008 - 2000 + 1 = 9[/tex]
[tex]T_n = Salary\ in\ 2008 = \$1,331,948[/tex]
Substitute these in the given formula
[tex]\$1,331,948 = \$446,600 + (9 - 1) d[/tex]
[tex]\$1,331,948 = \$446,600 + 8d[/tex]
Collect Like Terms
[tex]\$1,331,948 - \$446,600 = 8d[/tex]
[tex]\$885348 = 8d[/tex]
Divide both sides by 8
[tex]d = \$110668.5[/tex]
The linear equation is generated as follows;
[tex]T_n = a + (n - 1) d[/tex]
In this case;
[tex]a = Salary\ in\ 2000 = \$446,600[/tex]
[tex]d = \$110668.5[/tex]
[tex]T_n = y[/tex]
[tex]n = x[/tex]
Substitute these in the given formula
[tex]y = \$446,600 + (x - 1) * \$110668.5[/tex]
Open bracket
[tex]y = \$446,600 + \$110668.5x - \$110668.5[/tex]
Collect Like Terms
[tex]y = \$446,600 - \$110668.5 + \$110668.5x[/tex]
[tex]y = \$335931.5 + \$110668.5x[/tex]
Hence, the linear equation is
[tex]y = \$335931.5 + \$110668.5x[/tex]
