Math help?? graphing

if you get statement, for example, -x>6y
how do you know which way to shade the graph , not just this problem but in general..i know if the statement is false shade the opposite direction .but how you the statement is false

First you have to find the boundary of the area to shade. That's the line -x=6y or y = -x/6. So this is a line through the origin, with slope -1/6.

To see which side to shade, pick a point on one side of the boundary line, say (1,1) and plug in x=1 and y=1. If that satisfies the inequality, that's the side you shade. If it doesn't, you want the other side.

So it's very simple. Just pick a point and plug it in to see.