To find the equation of the perpendicular bisector of the line segment connecting the points (3,2) and (-1,7), we first need to find the midpoint of the line segment and the slope of the line segment.

The midpoint of the line segment is:

((3 - 1)/2, (2 + 7)/2) = (1, 4.5)

The slope of the line segment is:

(7 - 2) / (-1 - 3) = -5/4

The perpendicular bisector of the line segment will have a negative reciprocal slope of -4/5 and will pass through the midpoint of the line segment, (1, 4.5).

Therefore, the equation of the perpendicular bisector of the line segment is:

y - 4.5 = -4/5 (x - 1)

5y - 22.5 = -4x + 4

5y = -4x + 26.5

y = -\frac{4}{5} x + \frac{26.5}{5}

or

y = -0.8x + 5.3