A cashier earns $[tex]7[/tex] an hour. If [tex]x[/tex] is the number of hours worked, which function represents the cashier's earnings?
[tex]y=7 x[/tex]
[tex]y=x^7[/tex]
[tex]y=\frac{7}{x}[/tex]
[tex]y=7[/tex]
Answer (1)
The cashier earns $7 for every hour worked.
Let x represent the number of hours worked and y represent the total earnings.
The total earnings y is calculated by multiplying the hourly rate by the number of hours: y = 7 x .
The function representing the cashier's earnings is y = 7 x .
Explanation
Problem Analysis Let's analyze the problem. We are given that a cashier earns $7 per hour. We need to find a function that represents the cashier's total earnings, denoted by y , based on the number of hours worked, denoted by x .
Determining the Relationship The cashier's earnings are directly proportional to the number of hours worked. This means that for every hour the cashier works, they earn $7. Therefore, the total earnings y can be calculated by multiplying the hourly rate ($7) by the number of hours worked ( x ).
Formulating the Function We can express this relationship as a function: y = 7 × x , which simplifies to y = 7 x . This equation represents the cashier's earnings as a function of the number of hours worked.
Final Answer Therefore, the function that represents the cashier's earnings is y = 7 x .
Examples
Imagine you're saving up to buy a new video game that costs $63. If you earn $7 per hour as a cashier, the equation y = 7 x helps you calculate how many hours you need to work to afford the game. By substituting y = 63 , you can solve for x to find the number of hours: 63 = 7 x , so x = 9 hours. This shows how understanding this simple linear function can help you manage your time and money effectively.
