Step 1 :Given data points are (1991, 266000) and (2001, 1370000).
Step 2 :Find the slope of the line, which is the change in salary divided by the change in years. The slope is \(\frac{1370000 - 266000}{2001 - 1991} = 110400.0\).
Step 3 :Use one of the points to find the y-intercept of the line, which is the salary when the year is 0. The y-intercept is \(266000 - 110400 \times (1991 - 0) = -219540400.0\).
Step 4 :The linear function that fits the data is \(S(x) = 110400x - 219540400\), where \(x\) is the year.
Step 5 :Predict the average salary in 2005 by substituting 2005 into the function: \(S(2005) = 110400 \times 2005 - 219540400 = 1811600.0\).
Step 6 :Predict the average salary in 2010 by substituting 2010 into the function: \(S(2010) = 110400 \times 2010 - 219540400 = 2363600.0\).
Step 7 :Final Answer: The predicted average salary for 2005 is \(\boxed{\$1,811,600}\) and for 2010 is \(\boxed{\$2,363,600}\).