The relationship between the amount of a person's paycheck \( p \) and the number of hours worked \( t \) can be expressed as a direct variation. That means we can write the equation in the form:
\[ p = kt \]
where \( k \) is the constant of variation.
From the information given, when \( t = 10 \) hours, \( p = 57.50 \). We can use this to find \( k \):
\[ 57.50 = k \cdot 10 \]
To find \( k \), divide both sides by 10:
\[ k = \frac{57.50}{10} = 5.75 \]
Now, we can write the equation for the relationship:
\[ p = 5.75t \]
Therefore, the correct equation from your options is:
p = 5.75t