Answer:
[tex]y=-\frac{2}{5}x-3[/tex]
Step-by-step explanation:
First, you must find the midpoint of the segment, the formula for which is [tex](\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})[/tex]. This gives you (-5,-1) as the midpoint. This is the point at which the segment will be bisected.
Next, since we are finding a perpendicular bisector, we must determine what slope is perpendicular to that of the existing segment. To determine the segment's slope, we use the slope formula [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1}}[/tex], which gives us a slope of [tex]\frac{5}{2}[/tex].
Perpendicular lines have opposite and reciprocal slopes. The opposite reciprocal of [tex]\frac{5}{2}[/tex] is [tex]-\frac{2}{5}[/tex].
We now know that the perpendicular travels through the point (-5,-1) and has a slope of [tex]-\frac{2}{5}[/tex].
Solve for [tex]b[/tex] in [tex]y=mx+b[/tex].
[tex]y=mx+b\\-1=-\frac{2}{5}(-5)+b\\-1=2+b\\-3=b\\b=-3[/tex]
Therefore, the equation of the perpendicular bisector is [tex]y=-\frac{2}{5}x-3[/tex].
