4. Draw a line $l$ through the point $P(1,1)$ such that the midpoint of the chord intercepted by the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ is exactly $P$, then the equation of the line $l$ is $\qquad$
$\qquad$ \%.
4. $4 x+9 y=13$ Detailed Explanation: Let the equation of line $l$ be $y=k(x-1)+1$, substituting into the ellipse equation, and rearranging gives $\left(9 k^{2}+4\right) x^{2}+$ $18 k(1-k) x+9 k^{2}-18 k-27=0$. Let the two roots be $x_{1}, x_{2}$, then $\frac{x_{1}+x_{2}}{2}=1$, i.e., $-\frac{18 k(1-k)}{9 k^{2}+4}=2, \quad k=-\frac{4}{9}$. Therefore, the equation of line $l$ is $y=-\frac{4}{9}(x-1)+1$, which simplifies to $4 x+9 y=13$.