To determine the correct equation representing the earnings of someone making [tex]$12.75 per hour, let's analyze each option step-by-step.
1. Identify the variables:
- \(x\) represents the number of hours worked.
- \(y\) represents the total earnings in dollars.
2. Translate the given information into a mathematical relationship:
- If someone makes $[/tex]12.75 per hour, the total earnings ([tex]\(y\)[/tex]) is obtained by multiplying the hourly wage ([tex]$12.75) by the number of hours worked (\(x\)).
- Mathematically, this relationship can be expressed as
\[
y = 12.75 \times x
\]
3. Evaluate the given options:
- Option A: \(y = 12.75 + x\)
This implies that the total earnings are the sum of $[/tex]12.75 and the number of hours worked. This does not correctly represent an hourly wage situation.
- Option B: [tex]\(y = 12.75x\)[/tex]
This correctly translates the relationship between hours worked and total earnings, matching the equation we derived above.
- Option C: [tex]\(y = \frac{12.75}{x}\)[/tex]
This implies that the total earnings decrease as the number of hours worked increases, which does not match a direct multiplication relationship.
- Option D: [tex]\(x = 12.75y\)[/tex]
This suggests that the number of hours worked is proportional to the total earnings multiplied by [tex]$12.75, which implies incorrect representation of the hourly wage concept.
4. Conclusion:
The correct equation that corresponds to the earnings of someone who makes $[/tex]12.75 an hour is
[tex]\[
y = 12.75x
\][/tex]
Thus, the correct answer is Option B.
