Answer: Provided the three coordinate points, we have to find the equation of the perpendicular bisector of the provided line in slope intercept form:
[tex]\begin{gathered} y(x)=mx+b \\ \\ m=\frac{\Delta y}{\Delta x} \end{gathered}[/tex][tex](-5,-3)\text{ }(-1,-2)\text{ }(3,-1)[/tex]
Equation of the line and the perpendicular bisector:
[tex]\begin{gathered} m=\frac{\Delta y}{\Delta x}=\frac{-2-(-1)}{-1-3}=\frac{-1}{-4}=\frac{1}{4} \\ \\ m=\frac{1}{4} \\ \\ \therefore\rightarrow \\ \\ y(x)=\frac{1}{4}x+b\rightarrow-3=\frac{1}{4}(-5)+b\rightarrow b=-3+\frac{5}{4}=-\frac{7}{4} \\ \\ \therefore\rightarrow \\ \\ y(x)=\frac{1}{4}x-\frac{7}{4} \end{gathered}[/tex]
Therefore the perpendicular bisector is as follows:
[tex]\begin{gathered} \text{ Perpendicular bisector:} \\ \\ y(x)=\frac{1}{4}x-\frac{7}{4}\rightarrow y(x)=-4x+b \\ \\ \text{ Point of Bisection: }\Rightarrow(x,y)=(-1,-2) \\ \\ \therefore\rightarrow \\ \\ -2=-4(-1)=b\rightarrow b=-2-4=-6 \\ \\ \text{ Finaly the answer is:} \\ \\ y(x)=-4x-6 \end{gathered}[/tex]
Plot confirmation:
