The table lists average annual cost (in dollars) of tuition and fees at private four-year colleges for selected years.

(a) Determine a linear function ƒ(x) = ax + b that models the data, where x = 0 represents 2009, x = 1 represents 2010, and so on. Use the points (0, 22,036) and (4, 24,525) to graph ƒ and a scatter diagram of the data on the same coordinate axes. (Use a graphing calculator if desired.) What does the slope of the graph indicate?

(b) Use the function from part (a) to approximate average tuition and fees in 2012. Compare the approximation to the actual figure given in the table, $23,460.

(c) Use the linear regression feature of a graphing calculator to find the equation of the line of best fit.

Year.......................Cost (in dollars)

2009............................22,036

2010............................21,908

2011............................22,771

2012............................23,460

2013............................24,525