To determine the correct equation that models the wages of someone who makes [tex]$11.50 per hour, let's break down the components involved.
1. Total Earnings ($[/tex]y[tex]$) and Hours Worked ($[/tex]x[tex]$):
- $[/tex]y[tex]$ represents the total earnings in dollars.
- $[/tex]x[tex]$ represents the number of hours worked.
2. Rate of Pay:
- The rate of pay is $[/tex]11.50 per hour. This means for each hour worked, the person earns [tex]$11.50.
3. Equation Structure:
- In general, if someone earns a fixed rate per hour, the total earnings ($[/tex]y[tex]$) can be calculated by multiplying the hourly rate by the number of hours worked ($[/tex]x[tex]$).
4. Formulating the Equation:
- To find the total earnings, we multiply the hourly rate ($[/tex]11.50[tex]$) by the number of hours worked ($[/tex]x[tex]$).
Thus, the equation that models the total earnings as a function of the number of hours worked would be:
\[ y = 11.50x \]
Now, let's match this to the given options:
- A. \( y = 1150x \) (This implies earning $[/tex]1150 per hour, which is incorrect.)
- B. [tex]\( x = 11.50x \)[/tex] (This is incorrect as it does not relate earnings to hours worked correctly.)
- C. [tex]\( x = 1150x \)[/tex] (This is incorrect as it is not even solving for [tex]$y$[/tex], and the multiplication factor is incorrect.)
- D. [tex]\( y = 11.50x \)[/tex] (This correctly represents earning $11.50 per hour.)
Therefore, the correct equation is:
[tex]\[ \boxed{D. \, y = 11.50x} \][/tex]
