please help (creating linear equation question)

Question

The income per person over time for the United States is an approximately linear relation after 1950.

(a) In 1952, the income per person in the United States was about $17 000. In 2011, the

income per person was about $50 000. Create a linear equation to model the income

per person over time, where time is the number of years after 1920. (This means time

zero is 1920.) Round numbers to the nearest whole number for your equation.

(b) Using this equation, what would be the income per person in the year 2030?

(c) What year would the income per person be $150 000?

Answer 1

maybe think of this as two points on a graph (x,y) = (32,17) and (91,50) with y measured in thousands and x=0 as 1920

calculate the slope: (50-17)/(91-32) = 33/59= m

y=mx + b

y=(33/59)x + b where b is the y intercept. plug in either point to solve for b

17 = (33/59)(32) + b

b = 17 - (32)(33/59) = about -18 + 17 = -1

b=-1

y= (33/59)x-1

in 2030, t = 110 and y=(33/59)110 -1 = 3630/59-1 = about $61,524 income in 2030

150 = (33/59)x -1

151 = 33x/59

x = (59/33)151 = about 270 = 1920 + 270 = the year 2190