To find the constant of proportionality, we can use the formula for direct variation, which is:
\[ y = kx \]
where \( y \) is the amount of money earned, \( x \) is the number of hours worked, and \( k \) is the constant of proportionality (the earnings per hour).
From the problem, we know that Sarah earns $320 for working 40 hours. We can substitute these values into the formula:
\[ 320 = k \times 40 \]
To find \( k \), we can solve for it:
\[ k = \frac{320}{40} \]
Calculating this gives:
\[ k = 8 \]
Thus, the constant of proportionality, or Sarah's earnings per hour, is $8 per hour.