1. As shown in the figure, in the Cartesian coordinate system, the coordinates of vertex $B$ of rectangle $O A B C$ are $(5,4)$. If the line $y=k x+3 k$ exactly divides the rectangle $O A B C$ into two parts with an area ratio of $11: 13$, then the minimum value of the y-coordinate of the intersection point of this line with the $y$-axis is $\qquad$