Certainly! Let's break down the given information step by step to formulate an equation for the price [tex]\( y \)[/tex] of a cab ride that is [tex]\( x \)[/tex] miles long.
1. Flat Fee: The cab charges a fixed fee regardless of the distance traveled. This flat fee is [tex]$3.00. This component of the cost does not change and will be part of every fare calculation.
2. Per Mile Charge: In addition to the flat fee, the cab charges $[/tex]0.10 for every mile traveled. This means that for any number of miles [tex]\( x \)[/tex], the total charge for the distance traveled will be [tex]$0.10 multiplied by \( x \).
3. Combining the Costs: To determine the total cost \( y \) of the cab ride, we need to combine the flat fee with the charge per mile. The flat fee is a constant $[/tex]3.00, and the charge per mile can be represented as [tex]$0.10 multiplied by the number of miles \( x \).
Putting it all together, we can write an equation to model the price \( y \) as follows:
\[ y = \text{flat fee} + (\text{per mile charge} \times \text{number of miles}) \]
Substituting the given values:
\[ y = 3.00 + (0.10 \times x) \]
Therefore, the equation to model the price \( y \) of an \( x \)-mile-long cab ride is:
\[ y = 3.00 + 0.10x \]
This equation tells us that the total price for a cab ride consists of a $[/tex]3.00 base fee plus an additional $0.10 for each mile traveled.
