To write the equation for the perpendicular bisector of a segment, you need to know the slope of the segment and its midpoint.

The midpoint is the average of the end coordinates.

((-6+6)/2, (-2+4)/2) = (0/2, 2/2) = (0, 1)

The slope of the line between the endpoints is the y difference divided by the x difference.

M = (4-(-2))/(6-(-6)) = 6/12 = 1/2

Your line has a slope that is the negative reciprocal of this, -1/(1/2) = -2.

The point-slope form of the equation for the line is

y-y1 = m(x-x1)

We have (x1, y1) = (0, 1), so the line is

y-1 = -2(x-0)

Adding 1 to both sides of the equation gives

The midpoint is the average of the end coordinates.

((-6+6)/2, (-2+4)/2) = (0/2, 2/2) = (0, 1)

The slope of the line between the endpoints is the y difference divided by the x difference.

M = (4-(-2))/(6-(-6)) = 6/12 = 1/2

Your line has a slope that is the negative reciprocal of this, -1/(1/2) = -2.

The point-slope form of the equation for the line is

y-y1 = m(x-x1)

We have (x1, y1) = (0, 1), so the line is

y-1 = -2(x-0)

Adding 1 to both sides of the equation gives