To express the relationship between hours worked \( t \) and the paycheck \( p \), we can use the concept of direct variation. The formula for direct variation is:
\[ p = kt \]
where \( k \) is the constant of proportionality.
Given that for 22 hours of work, the paycheck is $126.50, we can substitute these values into the equation to find \( k \):
\[ 126.50 = k \times 22 \]
To find \( k \), we divide both sides by 22:
\[ k = \frac{126.50}{22} = 5.75 \]
Now, we can write the equation that relates the hours of work to the paycheck:
\[ p = 5.75t \]
This equation shows that the paycheck \( p \) varies directly with the number of hours worked \( t \) at a rate of $5.75 per hour.