Find the value of a so that f(x)=ax + b models the data. (round to one decimal place as needed)

Question

In 1992 ​, the average family income was about ​$41,000 ​, and in 2007 it was about $60,000.

(a) Let x=0 represent 1992, x=1 represent 1993, and so on. Find values for a and b so that f(x) = ax+b models the data.

(b) Estimate the average family income in 2002.

Answer 1

(0,41000) and (15,60000)

The slope is (60000-41000)/(15-0) = 19000/15 = 1266 and 2/3 = 3800/3

note that (0,41000) is also the y-intercept, where x is always zer0

f(x) = (3800/3)x + 41000