Step 1
Find the slope of the given line
Let
[tex]A(-5,-3)\ B(3,-1)[/tex]
we know that
The formula to calculate the slope between two points is equal to
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
substitute the values
[tex]m=\frac{-1+3}{3+5}[/tex]
[tex]m=\frac{2}{8}[/tex]
[tex]m=\frac{1}{4}[/tex]
Step 2
Find the slope of the perpendicular bisector
we know that
If two lines are perpendicular, then the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
In this problem
[tex]m1=\frac{1}{4}[/tex] -----> slope of the given line
Find m2
[tex]m2=-1/m1[/tex]
substitute
[tex]m2=-1/(1/4)=-4[/tex]
Step 3
Find the equation of the perpendicular bisector
we have
[tex]m2=-4[/tex]
point[tex](-1,-2)[/tex]
The equation of the line into slope-intercept form is equal to
[tex]y=mx+b[/tex]
substitute the values and find the value of b
[tex]-2=(-4)(-1)+b[/tex]
[tex]-2=4+b[/tex]
[tex]b=-6[/tex]
the equation of the line is
[tex]y=-4x-6[/tex]
therefore
the answer is the option B
[tex]y=-4x-6[/tex]
see the attached figure to better understand the problem
