Finding the funtion

Question

How do you find the function with the following points (1,9) (2,10.5), (3,13) (4,14.50)

Answer 1

Each time that x increases by 1, y increases by 1.5.  So, the points lie on a line of slope m = 1.5.

 

Equation of line:  y = mx+b

 

                         y = 1.5x + b

 

Since (1,9) is a point on the line, 9 = 1.5(1) + b

 

                                               b = 7.5

 

So, the function is:  f(x) = 1.5x + 7.5