Since the paycheck \( p \) varies directly with the number of hours worked \( t \), we can express this relationship mathematically as:
\[ p = kt \]
where \( k \) is the constant of variation.
To find \( k \), we can use the information given about the paycheck for 22 hours of work:
\[ 126.50 = k \cdot 22 \]
Solving for \( k \):
\[ k = \frac{126.50}{22} = 5.75 \]
Now that we have the value of \( k \), we can write the equation that relates the hours worked to the pay:
\[ p = 5.75t \]
This is the equation that describes the relationship between hours of work and pay.