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Answer:
[tex]f(x) = 1500x +3000[/tex]
Step-by-step explanation:
Given
Represent the months with x and the earnings with y.
So:
[tex](x_1,y_1) = (1,4500)[/tex]
[tex](x_2,y_2) = (2,6000)[/tex]
Required
Determine the linear function
First, calculate slope (m)
[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]
[tex]m = \frac{6000 - 4500}{2 - 1}[/tex]
[tex]m = \frac{1500}{1}[/tex]
[tex]m = 1500[/tex]
The equation is then calculated using:
[tex]y = m(x - x_1) + y_1[/tex]
[tex]y = 1500(x - 1) + 4500[/tex]
[tex]y = 1500x - 1500 + 4500[/tex]
[tex]y = 1500x +3000[/tex]
As a function, we have:
[tex]f(x) = 1500x +3000[/tex]