Question

The given line segment has a midpoint at (−1, −2).

Answer 1

The answer is B- y = −4x − 6

Answer 2

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