2. Among all lines passing through the point $\left(10, \frac{1}{2}\right)$, the number of lines that pass through at least two lattice points is $($ )
A. one
B. none
C. a finite number but no less than 2
D. infinitely many
2. D For any $m \in \mathbf{Z}$, the line $m(2 y-1)=x-10$ passes through the point $\left(10, \frac{1}{2}\right)$, and also through the lattice point $(10+$ $m(2 t-1), t)(t \in \mathbf{Z})$. Therefore, by the arbitrariness of $m$, we know that there are infinitely many such lines.