The table lists data regarding the average salaries of several professional athletes in the years 1991 and 2001. a) Use the data points to find a linear function that fits the $\begin{array}{cc}\text { Year } & \text { Average Salary } \\ 1991 & \$ 266,000 \\ 2001 & \$ 1,370,000\end{array}$ data. b) Use the function to predict the average salary in 2005 and 2010. A linear function that fits the data is $S(x)=$ (Let $x=$ the number of years since 1990 , and let $S=$ the average salary $x$ years from 1990.)

Step 1 ：We are given two points on the line: (1, 266000) and (11, 1370000).

Step 2 ：We can use these points to find the slope of the line, which is given by the formula: \(m = \frac{y_2 - y_1}{x_2 - x_1}\), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Step 3 ：Substituting the given points into the formula, we find that the slope of the line is 110400.

Step 4 ：Once we have the slope, we can use the point-slope form of a line to find the equation of the line: \(y - y_1 = m(x - x_1)\).

Step 5 ：We can then substitute one of the points and the slope into this equation to find the equation of the line.

Step 6 ：Doing this, we find that the y-intercept is 155600.

Step 7 ：This means that the linear function that fits the data is: \(S(x) = 110400x + 155600\).

Step 8 ：This function represents the average salary $S$ in the year $x$, where $x$ is the number of years since 1990.

Step 9 ：\(\boxed{S(x) = 110400x + 155600}\) is the final answer.