# If a line has no y intercept, can it be described by a function?

It can be described by an equation of the form $x = a$, but not by a function.
If a line has no $y$ intercept, then it can only be parallel to the $y$ axis and therefore has an equation of the form $x = a$ for some constant $a$.
A vertical line fails the vertical line test, has undefined slope and cannot be expressed as a function of $x$.