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
SHOW YOUR WORK!!
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
To find the rate of change and initial value for Sarah's business, we can use the formula for the slope of a line:
Slope (rate of change) = (change in y) / (change in x)
In this case, x represents the number of years since 2010 and y represents the annual dog-walking fee.
Using the given values:
change in x = 2014 - 2010 = 4 years
change in y = $750 - $350 = $400
Slope (rate of change) = (change in y) / (change in x) = $400 / 4 years = $100 per year
The initial value can be found by taking any point from the table. Let's take the point (2010, $350):
Initial value = $350
Thus, the rate of change is $100 per year and the initial value is $350.
To write an equation in slope-intercept form (y = mx + b) to represent the fees that Sarah charges each year:
y = mx + b
y = $100x + $350