To write the equation that represents the relationship between the number of eggs \( y \) and the amount of flour \( x \), we start with the information given: for every 3 cups of flour, you need to add 2 eggs.
This means that the ratio of eggs to flour is 2 eggs for every 3 cups of flour. In mathematical terms, we can express this as:
\[ \frac{y}{x} = \frac{2}{3} \]
From this, we can derive the equation relating \( y \) and \( x \):
\[ y = \frac{2}{3} x \]
This equation represents a proportional relationship because it is of the form \( y = kx \) where \( k \) (the constant of proportionality) is \( \frac{2}{3} \).
So the correct response is: \( y = \frac{2}{3}x \), proportional.