Cab companies often charge a flat fee for picking someone up and then charge an additional fee per mile driven. Pick a U.S. city and research the rates of two different cab companies in that city. Find companies that charge different amounts per mile and have different flat fees.
Task 1
a. For the first company, express in words the amount the cab company charges per ride and per mile.
b. Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did.
c. What do the x-intercept and y-intercept mean in the context of this problem? Hint: What do you pay when you step into the cab?
Task 2
For the second company, express in a table the cost of the cab ride given the number of miles provided.
Number 0 1 2 3 4 5 of Miles
a. Write an equation in slope-intercept, point-slope, or standard form. Explain why you chose the form you did.
b. What does the slope mean in the context of the problem?
Task 3
Cabs use a valuable commodity—gas! Research average gas prices from 2005– 2015 for the city you chose.
a. Create a table showing the average gas price each year. b. Create a scatter plot of the data in your table.
For Task 1, let's say we are looking at cab companies in New York City.
Company A charges a flat fee of $3.50 for the ride and an additional $2.50 per mile driven.
a. Company A charges $3.50 per ride and $2.50 per mile.
b. Let's write the equation in slope-intercept form.
The equation would be: y = 2.50x + 3.50
We chose slope-intercept form because it clearly represents the slope (the cost per mile) and the y-intercept (the flat fee for the ride).
c. In this context, the x-intercept represents the number of miles driven when the cost of the ride becomes zero. Since that is not possible in this case (as there will always be a flat fee), the x-intercept does not have a meaningful interpretation. The y-intercept represents the cost of the ride when no mileage has been driven, which is the flat fee of $3.50 that you pay when you step into the cab.
For Task 2, let's consider Company B.
Number of Miles: 0 1 2 3 4 5
Cost of Cab Ride: $5 $8 $11 $14 $17 $20
a. Based on the given table, the equation representing the cost of the cab ride (y) based on the number of miles (x) would be:
y = 3x + 5
We chose slope-intercept form because it allows us to clearly represent the slope (the cost per mile) and the y-intercept (the flat fee for the ride).
b. In this context, the slope represents the increase in cost for each additional mile driven.
For Task 3, let's research average gas prices in New York City between 2005-2015.
Year: 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Gas Price: $2.41 $2.65 $3.03 $3.35 $2.37 $2.83 $3.65 $3.87 $3.50 $3.37 $2.43
To create a scatter plot, we will plot the year on the x-axis and the gas price on the y-axis. Each point will represent the average gas price for a specific year.