find the equation in slope intercept form of the line that is the perpendicular bisector of the segment.

between (-3,4) and (3,-8)

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The slope of the line through (-3,4) and (3,-8) is

`(-8-4)/(3-(-3))=-12/6=-2`

To get a line perpendicular to that, we need the negative reciprocal of

`-2/1` , which is `1/2`

So, our line will have slope 1/2

We want to bisect the line segment, so we need to find its midpoint. We do that by taking the average of the x-values, and the average of the y-values:

`(-3+3)/2 = 0` , `(4-8)/2=-2`

Thus, we want our line to go through the point (0,-2)

We have a slope, and a point, so the equation of our line (in point-slope form) is:

`y+2 = (1/2)(x-0)`

In slope-intercept form, this is:

`y=(1/2)x -2`

The graph looks like:

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