1. The problem asks for a line parallel to the vertical line $x=1$ passing through the point $(3,2)$. 2. Lines parallel to $x=1$ are also vertical lines, meaning they have the equation $x = k$ where $k$ is a constant. 3. Since the new line must pass through $(3, 2)$, it must have $x=3$ (the $x$ coordinate of the point). 4. Therefore, the equation of the line parallel to $x=1$ and passing through $(3, 2)$ is: $$x=3$$