To find the correct equation that represents the total earnings in dollars ([tex]\(y\)[/tex]) based on the hours worked ([tex]\(x\)[/tex]) at an hourly wage of [tex]$10.25, we need to match the equation with the scenario given.
Let's analyze each option:
A. \(y = 10.25x\)
In this option, \(y\) is calculated by multiplying the hourly wage (\$[/tex]10.25) by the number of hours worked ([tex]\(x\)[/tex]). This representation makes sense because earnings are the product of the hourly wage and the total hours worked.
B. [tex]\(x = 10.25y\)[/tex]
Here, [tex]\(x\)[/tex] (hours worked) is calculated by multiplying the earnings ([tex]\(y\)[/tex]) by the hourly wage (\[tex]$10.25). This does not accurately describe the relationship we are looking for since the roles of earnings and hours worked are inverted.
C. \(y = 10.25 + x\)
In this option, the total earnings (\(y\)) are given by adding the hourly wage (\$[/tex]10.25) to the number of hours worked ([tex]\(x\)[/tex]). This is incorrect because we should be multiplying, not adding.
D. [tex]\(y = \frac{10.25}{x}\)[/tex]
Here, the total earnings ([tex]\(y\)[/tex]) would be the result of dividing the hourly wage (\$10.25) by the number of hours worked ([tex]\(x\)[/tex]). This does not make sense in the context of earnings since earnings should increase with more hours worked, not decrease.
Given this analysis, the correct equation is:
A. [tex]\(y = 10.25x\)[/tex]
So the answer is:
1 (corresponding to option A).
