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. If you have trouble finding this information for two companies, you can make up what you think would be reasonable prices for a cab's flat rate and a cab's rate per mile.
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. Whatdotheslopeandy-interceptmeaninthecontextofthisproblem? Hint: What do you pay when you step into the cab?
I will research the rates of two different cab companies in the city of New York.
Company A charges a flat fee of $3.50 for picking someone up and an additional fee of $2.50 per mile driven.
a. The first company charges a flat fee of $3.50 per ride and an additional fee of $2.50 per mile.
b. Let x be the number of miles driven.
The equation that represents the total cost (y) for Company A can be written as:
y = 3.50 + 2.50x
I chose slope-intercept form (y = mx + b) because it is straightforward and easy to understand, where m represents the rate per mile (slope) and b represents the flat fee (y-intercept).
c. In this context, the slope (2.50) represents the rate at which the cost increases per mile driven. The y-intercept (3.50) represents the base cost or the amount you pay when you step into the cab, regardless of the distance traveled.