Question

Elliot has been running a lawn care business since 2000. He cuts grass, trims, and weed whacks yards for his customers throughout the season. Each year, he has increased his fee by the same amount. The table shows what Elliot charged each customer for two given years of his business:
Year Lawn Care Fee
2000 $750
2010 $1350


A. What is the rate of change and initial value for Elliot’s business? How do you know?
B. Write an equation in slope-intercept form to represent the fees that Elliot charges each year.

Answer 1

A.) Rate of change = (1350 - 750) / (2010 - 2000) = 600/10 = $60
The initial value is the amount he charged in his first year of business which is $750.

B.) Required equation is given by y - 750 = 60x
y = 60x + 750 where x represent the number of years after 2000.