Answer: [tex]y-\frac{11}{2}=6(x-2)[/tex]
Step-by-step explanation:
For it to bisect the segment, we need to find the midpoint.
The midpoint is [tex]\left(\frac{-1+5}{2}, \frac{6+5}{2} \right)=\left(2, \frac{11}{2} \right)[/tex].
Now, for it to be perpendicular, we need to use the fact that perpendicular lines have slopes that are negative reciprocals of each other.
The slope of the given segment is [tex]\frac{6-5}{-1-5}=-\frac{1}{6}[/tex], so the slope of the perpendicular bisector is 6.
Thus, the equation of the line in point-slope form is [tex]\boxed{y-\frac{11}{2}=6(x-2)}[/tex]
