7. 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 $\qquad$ .
$=, 7.4 x+9 y=13$.
Let the equation of line $l$ be $y=k(x-1)+1$.
Substituting into the ellipse equation and rearranging, we get
$$
\left(9 k^{2}+4\right) x^{2}+18 k(1-k) x+9 k^{2}-18 k-27=0 \text {. }
$$

Let the two roots be $x_{1} 、 x_{2}$. Then $\frac{x_{1}+x_{2}}{2}=1$, i.e.,
$$
-\frac{18 k(1-k)}{9 k^{2}+4}=2 \Rightarrow k=-\frac{4}{9} \text {. }
$$

Therefore, the equation of line $l$ is $y=-\frac{4}{9}(x-1)+1$, i.e., $4 x+9 y=13$