Final answer:
Yes. Taxi fares exhibit a proportional relationship when the fare is calculated based on a constant rate per unit distance, such as $2.50 per mile. If there is also a fixed base charge, the relationship deviates from being purely proportional but the variable charge remains a proportional part of the overall fare.
Step-by-step explanation:
Whether taxi fares are an example of a proportional relationship can be determined by examining the way the fare is calculated. A proportional relationship exists when two quantities increase or decrease at the same rate. For a taxicab industry, if the fare is directly proportional to the distance traveled, this means that for each unit of distance, there is a constant rate being charged. This constant rate is referred to as the constant of proportionality.
For instance, if a taxi company charges $2.50 per mile, then a trip of 1 mile costs $2.50, a trip of 2 miles costs $5.00, and so on. In this case, the relationship between distance and fare is proportional because you can use the formula fare = $2.50 × distance to find the total fare. The fare increases by the same amount for each additional mile traveled.
However, if the fare included a fixed base charge in addition to a variable charge per mile, then the relationship would not be purely proportional because the total fare would not simply be the product of the distance and a constant rate. The initial fee would cause the relationship to deviate from a strict proportional model, particularly for shorter trips. Nonetheless, the variable part of the fee (e.g., per mile) can still be considered proportional to the distance traveled.