Final answer:
The equation that shows the number of rides as a function of the total cost is a) R = (C - 12)/4. This is the only choice that correctly represents the structure of a linear function as it implies a proportional relationship once the initial fee is accounted for.
Step-by-step explanation:
The question looks for the equation that describes the number of rides, R, as a function of the total cost, C. To answer this, we can approach the problem by considering the structure of the equation. A functional relationship between R and C would be linear if the relationship is direct without any exponents or squared terms, making it a linear equation which is usually given by the form y = mx + b, where m is the slope and b is the y-intercept.
Looking at the provided options:
- a) R = (C - 12)/4 represents a linear equation, which has been rearranged from the standard linear form. If we multiply through by 4, this option represents R as 4 being multiplied by C, subtracting a constant value of 12, and then dividing the whole by 4.
- b) R = (4C + 12) is not a function of C, since there is no operation shown. Presumably, this may be a typographical error.
- c) R = 4C - 12 is not a function that fits as the multiplication of C by 4 is not adjusted for any base rate or intercept.
- d) R = C/4 - 3 is a valid linear equation with C divided by 4 and then subtracting 3, fitting the structure of linear functions.
Considering standard form and the context likely provided by additional information on the cost per ride and a base fee, the equation that shows the number of rides as a function of the total cost is a) R = (C - 12)/4.