To find the y-intercept of a line given in the slope-intercept form \( y = mx + b \), we identify the value of \( b \). The y-intercept occurs where the line crosses the y-axis, which happens when \( x = 0 \).
In the equation \( y = \frac{8}{9}x + 2 \), the value of \( b \) is 2. Therefore, the y-intercept is:
\[ (0, 2) \]
So, the y-intercept of the line is \( 2 \).