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.

anonymous · Answer

For A i have the rate of change as 60 and the initial value 750. I need help on where it intersects for the equation.

danjs · Answer

They tell you it is a line by the wording "  Each year, he has increased his fee by the same amount."

danjs · Answer

fee is a function of the year

danjs · Answer

The table gives you two points on the line 
(x,y) = (2000, $750)
(x1,y1) = (2010. $1350)

danjs · Answer

You are correct, you calculated the slope as 60 dollars per year

$$m = \frac{ y - y1 }{ x-x1 } = \frac{ 750-1350 }{ 2000-2010 } = \frac{ -600 }{ -10 } = 60$$

danjs · Answer

Now use the Slope-Point form to put together the equation.

Slope m = 60
point (x1,y1) = (2000 , 750)

y - y1= m*(x-x1)

plug in the values and get the line

danjs · Answer

You can use either of the given points in the equatio