In the equation for direct variation \( y = kx \), where \( k \) is the constant of proportionality, your equation is given as \( y = 2 \frac{2}{3} x \).
To find the constant of proportionality, we need to express \( 2 \frac{2}{3} \) as an improper fraction:
\[ 2 \frac{2}{3} = \frac{2 \times 3 + 2}{3} = \frac{6 + 2}{3} = \frac{8}{3} \]
So, the constant of proportionality \( k \) is \( \frac{8}{3} \).
Since this value is not listed among the provided responses (which include \( 223, 2 \frac{2}{3}, 23, \frac{2}{3}, 3, 2 \)), it seems there is either a misunderstanding or misrepresentation of the equation itself.
However, if you are asking for the specific form \( 2 \frac{2}{3} \) rather than its value as an improper fraction, the answer would simply be \( 2 \frac{2}{3} \).
Therefore, the constant of proportionality in improper fraction form is \( \frac{8}{3} \), but if referring directly to the fractional form of the coefficient in the given equation, the answer is \( 2 \frac{2}{3} \).