Final answer:
The correct linear equation for the taxicab fees in New York City with a structure of $2.50 upon entry and $0.40 for each 1/5 of a mile is y = 0.40x + 2.50, which corresponds to option A). The fee structure indicates $0.40 as the cost per 1/5 mile (slope) added to the $2.50 entry fee (y-intercept).
Step-by-step explanation:
To find the linear equation representing the taxicab fees in New York City, we need to understand the components of the equation, y = mx + b. Here, y represents the total cab fare, x represents the number of miles traveled, m is the cost per mile (after the initial entry fee), and b is the initial entry fee.
Given the taxi fare structure, the initial fee upon entry is $2.50, which will be our y-intercept (b). Then, since a unit is 1/5 of a mile and the cost per unit is $0.40, we need to determine the cost per mile. Since there are 5 units in a mile (1 unit = 1/5 mile), the cost per mile is $0.40 * 5, which equals $2.00. However, this does not match with the given structure of the problem which states $0.40 per additional unit, not per mile. Thus, we keep the rate of $0.40 per 1/5 of a mile as the slope (m) of our equation.
With this information, the equation is y = 0.40x + 2.50, which corresponds to option A). This is because each mile (x) will add $0.40 for every 1/5 of a mile traveled to the initial fare of $2.50.