How to find the equation of the perpendicular bisector of y=-x+4

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A line that is perpendicular to another line has a slope that is the negative reciprocal.  Your lines slope is -1.  The negative reciprocal is 1.  Lines are infinitely long, but lets assume the perpendicular bisector bisects your line at its y intercept, which is (0, 4).  Thus the perpendicular bisector of your line is y = x +4

Except you can't bisect a line like y = -x + 4 which has infinite length.  You can only find the slope of any line perpendicular to it.  That slope is 1.