To find the slope of the line given in the equation \( y = \frac{2}{9}x + \frac{6}{13} \), we can identify the slope by examining the equation directly.
In the slope-intercept form of a line, \( y = mx + b \), \( m \) represents the slope and \( b \) represents the y-intercept.
From the equation:
\[ y = \frac{2}{9}x + \frac{6}{13} \]
Here, the coefficient of \( x \) (which is \(\frac{2}{9}\)) is the slope.
Thus, the slope of the line is:
\[ \frac{2}{9} \]
This is already in its simplest form. Therefore, the final answer is:
\[ \frac{2}{9} \]