Assuming that you are talking about the Cartesian plane, then an equation describing a vertical line isn't too difficult; it's simply x = c, where c is some constant. For example, x = 2 would describe a line passing through (2,0).

However, there is no _function_ for a vertical line because functions must map a point in the domain to only one point in the range. In this case, x represents values in the domain, and y represents values in the range. A vertical line, such as x = 2, would map the value 2 in the domain to more than one point in the range; in fact, it maps 2 to every single value in the range, thus contradicting the definition of a function.

Hope this helps,
Dave