If [tex]x[/tex] represents hours worked and [tex]y[/tex] represents total earnings in dollars, then the equation that corresponds to the earnings of someone who makes [tex]\$12.75[/tex] an hour is

A. [tex]y = 12.75 + x[/tex]
B. [tex]y = 12.75x[/tex]
C. [tex]y = \frac{12.75}{x}[/tex]
D. [tex]x = 12.75y[/tex]



Answer :

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.