Answer
$y = x-3$
Work Step by Step
We can find the midpoint of the line segment joining the two points:
$x = \frac{1+7}{2} = 4$
$y = \frac{4+(-2)}{2} = 1$
The midpoint is $(4,1)$
We can find the slope of the line segment joining the two points:
$m = \frac{4-(-2)}{1-7} = \frac{6}{-6} = -1$
The slope of the perpendicular bisector is $(-\frac{1}{m}) = 1$
Note that the perpendicular bisector passes through the point $(4,1)$
We can find an equation of the perpendicular bisector:
$y-1 = (1)(x-4)$
$y = x-4+1$
$y = x-3$
