To find the constant of proportionality \( k \) that relates Matthew's earnings \( y \) to the number of hours he worked \( x \), we can use the formula \( k = \frac{y}{x} \).
This means you need to know a specific pair of values for \( y \) (earnings) and \( x \) (hours worked).
For example, if Matthew earned $300 for 10 hours of work, you would calculate the constant of proportionality as follows:
\[ k = \frac{y}{x} = \frac{300}{10} = 30 \]
So the constant of proportionality \( k \) would be 30.
If you provide specific values for Matthew's earnings and hours worked, I can calculate \( k \) for those values.