A cashier earns $\$7$ an hour. If $x$ is the number of hours worked, which function represents the cashier's earnings?
The problem defines a relationship between the time spent working and total earnings. The cashier earns a fixed rate of \(\$7\) for every hour worked. Let \(x\) represent the number of hours worked, and \(y\) represent the total earnings in dollars. Since the earnings are directly proportional to the number of hours, we multiply the hourly rate by the number of hours to determine the total earnings.
The total earnings \(y\) are calculated by multiplying the hourly wage by the quantity of hours worked \(x\). This relationship is expressed as:
\[y = \text{rate} \times \text{hours}\]
Given that the hourly rate is \(\$7\), we substitute this into the equation:
\[y = 7 \times x\]
Thus, the function representing the cashier's total earnings is \(y = 7x\).
Comparing our derived function \(y = 7x\) with the provided options:
The correct representation is therefore the first option. The final answer is \(\boxed{y = 7x}\).
Understanding linear relationships like this is fundamental in daily life for tasks such as calculating wages based on hours worked, determining the cost of items based on quantity, or predicting distance traveled at a constant speed. For instance, if you purchase apples at a price of \(\$2\) each, the total cost \(C\) for \(n\) apples can be expressed by the linear function \(C = 2n\), demonstrating how math helps us manage finances and resources effectively.