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