Final answer:
The relationship between the total cost of a cab ride and the number of miles is defined by the linear equation C = 5 + 0.80m, where C represents the total cost, 5 is the fixed fee, and 0.80 is the cost per mile.
Step-by-step explanation:
The question asks to establish the relationship between the total cost of a cab ride and the number of miles m traveled. The cost equation of a cab ride is a linear equation, where the total cost is a combination of a fixed initial fee and a variable cost that depends on the distance traveled.
In this case, the fixed fee is $5, and the cost per mile is $0.80. Consequently, the equation that relates the total cost C (in dollars) to the number of miles m is:
C = 5 + 0.80m
Here, 5 represents the initial fee, and 0.80 is the cost for each additional mile. The equation follows the format of a linear function y = mx + b, where m is the slope and b is the y-intercept. In the context of the cab ride, m = 0.80 (slope), indicating the cost per mile, while b = 5 (y-intercept), which is the constant fee irrespective of miles traveled.