Neil has been running a tutoring business since 2005. He charges a monthly fee for weekly tutoring sessions and a phone help line. Each year, he has increased his fee by the same amount. The table shows what Neil charged each customer for two given years of his business:

Year Annual Tutoring Fee
2005 $1200
2008 $1350

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

Part A. Rate of change $ 50

The initial value of Neil's business is $ 1,200

Part B. x = 1200 + 50y

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Year Annual Tutoring Fee

2005        $ 1,200

2008        $ 1,350

2. What is the rate of change and initial value for Neil’s business? How do you know?

Rate of change = (Annual Tutoring Fee in 2008 - Annual Tutoring Fee in 2005)/(2008 - 2005)

Replacing with the values we have:

Rate of change = (1,350 - 1,200)/3

Rate of change = 150/3 = $ 50

The initial value of Neil's business is $ 1,200

3. Write an equation in slope-intercept form to represent the fees that Neil charges each year.

Let x to represent the the fees that Neil charges annually and y to represent the number of years after 2005, we have:

x = 1200 + 50y

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