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?
For Task 1:
Let's consider the city of New York and two cab companies - Company A and Company B.
a. For Company A, they charge a flat fee of $2.50 for picking someone up and an additional fee of $2.00 per mile driven.
b. Let's write an equation in slope-intercept form. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Let's denote the total cost of the ride as y and the distance traveled in miles as x. The equation for Company A can be written as:
y = 2.00x + 2.50
I chose slope-intercept form because it allows us to directly see the cost per mile (slope) and the initial cost when stepping into the cab (y-intercept).
c. In this problem, the x-intercept represents the distance at which the cost of the ride becomes $0. In reality, this does not have a practical meaning since you cannot ride for free. On the other hand, the y-intercept represents the initial cost when stepping into the cab. In this case, it is $2.50, which is the flat fee charged by Company A.