Question

Find the equation of a straight line which is equidistant from the points (2,3) and (6,1) expressing it in the form ax+by=c

Answer 1

the line through those two points has slope -1/2

the line containing all points equidistant from those two points will be the perpendicular bisector, which has slope 2
The midpoint is (4,2) so we want the line with equation
y-2 = 2(x-4)
y-2 = 2x-8
2x-y = 6