Example 1, in the ellipse $\frac{x^{2}}{16}+\frac{y^{2}}{12}=1$, find the equation of the line passing through $M(2,1)$ and bisecting at point I.
According to Theorem 3,
$$
\begin{array}{c}
\because k_{A B} \cdot k_{O M}=-\frac{12}{16}, \\
k_{O M}=\frac{1}{2}, \\
\therefore k_{A B}=-\frac{12}{16} \cdot 2=-\frac{3}{2} .
\end{array}
$$

Therefore, the equation of $A B$ is: $y-1=-\frac{3}{2}(x-2)$.