Question 82158
First find the midpoint of the segment with the endpoints (3,5) and (7,-3)


*[invoke Midpoint_of_segment_connecting_two_point 3, 5, 7, -3]


So we know that the bisecting line will go through the point (5,1). Now find the slope of the line going through (3,5) and (7,-3)


*[invoke slope 3, 5, 7, -3]


Since the slope of the line through (3,5) and (7,-3) is {{{m=-2}}} we know the perpendicular slope is 

{{{m[p]=-1/m}}} where {{{m[p]}}} is the perpendicular slope


{{{m[p]=-1/-2=1/2}}}


So the bisecting line has a slope of 1/2 and goes through the point (5,1). So lets find the equation of the line:


*[invoke find_line_by_slope_and_point 5, 1, 1/2]

So the equation of the bisecting line is 


{{{y=(1/2)x-3/2}}} or {{{y=0.5x-1.5}}}