Question

Sarah has been running a dog-walking business since 2010. She walks dogs twice a day, takes them to the park, and returns them to their homes. Each year, she has increased her fee by the same amount. The table shows what Sarah charged each customer for two given years of her business:
Year Annual Dog-walking Fee
2010 $350
2014 $750

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

Answer 1

350 + 4x = 750

x = the amount the fee went up annually. 

4x = 750 - 350
4x = 400
x = 400/4
x = 100

The rate of change is 100 dollars per year. The initial value of her business is 350 dollars. To check your work (aka how do you know) if you add 100 dollars to her initial value (350) 4 times you get 750.