Find a relationship between x and y such that (x, y) is equidistant from the two points: (2, 6), (7, −8)

Hello,

1) Finding the slope of the line passing throught the 2 points:

m=(-8-6)/(7-2)=-14/5.
A perpendicular line has a slope of -1/m=5/14

So the line searched has for equation:

y+1=(x-2)*5/14
or 10x-28y+73=0