It depends on what you mean by "undefined". If you mean that the slope is unknown then no, there are an infinite number of lines passing through a single point.
If you mean that the slope is of the form m = 1/0, then this is the case for a vertical line passing through the point (2,-8). The equation for this line is x = 2.
Let the required equation of a line be y =mx+c where m is any slope.
If this line passes through (x1,y1) then ,
(y- -8) = m(x-2) as (x1,y1)=(2,-8). Or
y=mx-2m+8 defines any straight line through (2,-8) for an desired slope.
Special cases when m is infinite:
If m is infinite, then 1/m = 0, then y/m=0 = x-2 or x-2 = 0 is a perpendicular line to x axis which passes through (2,-8)
Special case when m is zero:
If m= o, y=-8 is parallel to x axis.
Hope this helps.