Write the equation for the perpendicular bisector of the line segment connecting the points $(3,2)$ and $(-1,7)$ in the form $y = mx + b$.
Note: The perpendicular bisector of the line segment $\overline{AB}$ is the line that passes through the midpoint of AB and is perpendicular to AB.
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