Answer :
To find the correct equation that models the wages of someone who makes [tex]$6.25 an hour, let's break this down step-by-step.
1. Identify what the variables represent:
- \( y \) represents total earnings in dollars.
- \( x \) represents hours worked.
2. Relate the earnings to the hours worked:
- If someone makes $[/tex]6.25 an hour, the total earnings ([tex]\( y \)[/tex]) can be calculated by multiplying the number of hours worked ([tex]\( x \)[/tex]) by the wage per hour ([tex]$6.25).
3. Set up the equation:
- The total earnings (\( y \)) equal the hourly wage ($[/tex]6.25) times the number of hours worked ([tex]\( x \)[/tex]).
- This relationship is written as:
[tex]\[
y = 6.25 \times x
\][/tex]
4. Match this equation to the given options:
- Option A: [tex]\( x = 6.25x \)[/tex] is incorrect because it incorrectly places the total earnings ([tex]\( y \)[/tex]) on the left-hand side and also misrepresents the hourly relationship.
- Option B: [tex]\( y = 625x \)[/tex] is incorrect because it suggests that the hourly wage is [tex]$625 instead of $[/tex]6.25.
- Option C: [tex]\( x = 625y \)[/tex] is incorrect because it incorrectly switches the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] and also misrepresents the hourly relationship.
- Option D: [tex]\( y = 6.25x \)[/tex] is correct as it accurately models the relationship between hours worked and total earnings with the correct hourly wage.
Therefore, the correct equation is:
[tex]\[ \boxed{y = 6.25x} \][/tex]
This corresponds to option [tex]\( D \)[/tex].
1. Identify what the variables represent:
- \( y \) represents total earnings in dollars.
- \( x \) represents hours worked.
2. Relate the earnings to the hours worked:
- If someone makes $[/tex]6.25 an hour, the total earnings ([tex]\( y \)[/tex]) can be calculated by multiplying the number of hours worked ([tex]\( x \)[/tex]) by the wage per hour ([tex]$6.25).
3. Set up the equation:
- The total earnings (\( y \)) equal the hourly wage ($[/tex]6.25) times the number of hours worked ([tex]\( x \)[/tex]).
- This relationship is written as:
[tex]\[
y = 6.25 \times x
\][/tex]
4. Match this equation to the given options:
- Option A: [tex]\( x = 6.25x \)[/tex] is incorrect because it incorrectly places the total earnings ([tex]\( y \)[/tex]) on the left-hand side and also misrepresents the hourly relationship.
- Option B: [tex]\( y = 625x \)[/tex] is incorrect because it suggests that the hourly wage is [tex]$625 instead of $[/tex]6.25.
- Option C: [tex]\( x = 625y \)[/tex] is incorrect because it incorrectly switches the roles of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] and also misrepresents the hourly relationship.
- Option D: [tex]\( y = 6.25x \)[/tex] is correct as it accurately models the relationship between hours worked and total earnings with the correct hourly wage.
Therefore, the correct equation is:
[tex]\[ \boxed{y = 6.25x} \][/tex]
This corresponds to option [tex]\( D \)[/tex].
