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.

I only need help with part A.

Answer 1

for part A, we need to find the rate of change and initial values for Elliot's business. Because it states that Elliot started his business in 2000, we can use that for the initial value, meaning that on our graph, instead of starting at 2000, we can just start at 0. And for the rate of change, all we have to do is use the information given to set up the slope equation, which is (y2-y1)/(x2-x1). Because we know that the independent values usually go on the x-axis, we know that the years will be our x values, leaving the prices to be our y values. To set up the equation, we should have (1350-750)/(2010-2000), which should simplify to 600/10, which further simplifies to 60. This will be our slope!