A line parallel to the line y = x -4 would have a slope of 1.
A line perpendicular to the line y = x -4 would have a slope of -1.
Remember, parallel lines are lines that never intersect, which means that they cannot possibly have different slopes. A perpendicular line will <em>always</em> have the opposite slope as the first line, because the two lines must intersect at a 90 degree angle. The attached image shows how this works.