I put this problem in my graphing calculator but do not
come up with one of the 4 answers, here goes: 
The table below shows the number of doctors in Bingham 
City from 1960 to 1986. 
Year (x) 1960 1967 1970 1975 1982 1985 1986
Number of 2937 3511 3754 4173 4741 5019 5102
Doctors (y) 
If a linear regression model is fit to this data, which 
equation would best represent the data? 
(let x - number of years after 1960)

I punched STAT, then ENTER

Then I put 0, 7, 10 15, 22, 25, 26 in L1
and 2937, 3511, 3754, 4173, 4741, 5019, 5102 in L2

Then I punched STAT, right arrow, 4, ENTER and read

LinReg
 y=ax+b
 a=83.19520548
 b=2928.786204

so the linear regression equation is 

y = 83.19520548x + 2928.786204

Checking:

when x = 0, y = 2928.786204, compares well with 2937
when x = 7, y = 3511.152642, compares well with 3511
when x = 10, y = 3760.738259, compares well with 3754
when x = 15, y = 4176.714286, compares well with 4173
when x = 22, y = 4759.080725, compares well with 4741
when x = 25, y = 5008.666341, compares well with 5019 
when x = 26, y = 5091.861546, compares well with 5102

I'd say this as good a linear fit as you're going to get.

Edwin