To determine the constant of proportionality \( k \) that relates Matthew's earnings \( y \) to the number of hours he worked \( x \), you would use the formula \( k = \frac{y}{x} \).
This means that if you have a specific point (i.e., a certain number of hours worked and the corresponding earnings), you can plug those values into the formula.
For example, if Matthew worked 10 hours and earned $120, you would calculate it as follows:
\[ k = \frac{y}{x} = \frac{120}{10} = 12 \]
Thus, the constant of proportionality \( k \) would be $12 per hour.
Please provide the specific earnings and hours worked if you want me to calculate it with real numbers!