(7) Through the point $P(1,1)$, draw a line $l$ such that the midpoint of the chord it intercepts from the ellipse $\frac{x^{2}}{9}+\frac{y^{2}}{4}=1$ is exactly $P$. Then the equation of the line $l$ is . $\qquad$
(7) Let the equation of line $l$ be $y=k(x-1)+1$. Substituting into the ellipse equation and simplifying, we get
$$
\left(9 k^{2}+4\right) x^{2}+18 k(1-k) x+9 k^{2}-18 k-27=0,
$$

Let the two roots be $x_{1}$ and $x_{2}$, then $\frac{x_{1}+x_{2}}{2}=1$, which means
$$
-\frac{18 k(1-k)}{9 k^{2}+4}=2,
$$

Solving for $k$ gives $k=-\frac{4}{9}$, so the equation of line $l$ is
$$
y=-\frac{4}{9}(x-1)+1,
$$

which simplifies to $4 x+9 y=13$.