To represent the total amount Charlie charges her clients after the consultation fee and for \(x\) hours of personal training, we can formulate the equation based on the information provided.
Charlie charges a consultation fee of $18 and an hourly rate of $12. Thus, the total amount \(y\) that she charges can be expressed in the following equation:
\[ y = 18 + 12x \]
In this equation:
- \(y\) represents the total amount charged by Charlie.
- \(18\) is the one-time consultation fee.
- \(12\) is the hourly rate.
- \(x\) is the number of hours of personal training.