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.

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.

mhanifa · Answer

To find the rate of change 
1. Take the pairs as (x, y) values (2000, 750) as example
2. Find the difference of x and y values
3. Find the ratio of difference of y/ difference of x, this is the rate of change

mhanifa · Answer

This is same as finding the slope and you will get a slope of the equation you need. Initial value of y is the y-intercept.

mhanifa · Answer

To make it simpler you may drop 2000 from the both points, then you have pairs (0, 750) and (10, 1350)