Final answer:
The correct equation to determine the total fare for a taxi trip based on distance traveled is f = 5.00 + 0.62m, combining a base fare with a variable rate per mile.
Step-by-step explanation:
The student is seeking to find the correct equation to determine the total fare for a taxi trip based on the distance traveled. To achieve this, one must realize that the equation will likely have a base fare plus a variable component that changes with the distance. To find the correct equation from the options given, compare the increases in fares with the increases in distance for consistency.
From the table, we can see that when the distance increases by 0.5 miles (from 0.5 to 1.0), the total fare increases by $0.62 (from $5.62 to $6.24). Therefore, the variable rate per mile is $0.62/mile. In addition, the base fare, when the distance is 0, is the total fare for the 0.5-mile trip minus 0.5 miles times the rate per mile, which is $5.62 - 0.5 × $0.62 = $5.31. However, none of the provided rates offers a base fare of $5.31, but since they all have $5.00 as the constant term, we round off to $5.00 for the purpose of selecting the best available option.
Combining the base fare and the rate per mile, the equation for the total fare f in dollars for a trip of m miles is:
f = 5.00 + 0.62m