Is there a point slope form for a three dimensional line?
Not really, but...
Something vaguely similar that you can use for a line in any number of dimensions is a point-vector form, which you could write like this:
#underline(x) = underline(x_0)+tvec(v)#
In three dimensions:
#(x, y, z) = (x_0, y_0, z_0) + t(u, v, w)#
#= (x_0 + tu, y_0 + tv, z_0 + tw)#