The direct variation equation is of the form \( y = kx \), where \( k \) is the constant of proportionality. In the equation given, \( y = 2 \frac{2}{3} x \), we can identify the constant \( k \).
First, convert \( 2 \frac{2}{3} \) to an improper fraction: \[ 2 \frac{2}{3} = \frac{8}{3} \]
Thus, the equation can be written as: \[ y = \frac{8}{3} x \]
From this, we can see that the constant of proportionality \( k \) is \( \frac{8}{3} \).
Therefore, the answer is: 2 2/3