Oh okay. I think that what this is asking, is that they just want you to find the slopes.
So first you have to put both equations into y=mx+b form
So first equation, x-2y+8=0, now we subtract 8 on both sides aswell as subtract x and were left with -2y=-x-8 now we have to divide by negative two on both sides which gives you y=1/2x+4.
Then we do the same to the second equation. 2x+y+1=0. Se switch some things around and get Y=-2x-1
Okay so your answer would be something like this.
These lines are perpendicular since the slopes are the inverse of one another. The second like would run in the direction of the 4 quadrant. And the first in the direction of the 1st quadrant.