Can you write an equation of a line that goes through the point 2 and negative 8 if the slope is undefined? No

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-y1=m(x-x1)

(y- -8) = m(x-2) as (x1,y1)=(2,-8). Or

y+8=m(x-2). 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.