For the given line segment, write the equation of the perpendicular bisector.

Answer:[tex]y=-0.8x-4.7[/tex]Step-by-step explanation:Let[tex]A(-6,-4), B(-2,1)[/tex] we know thatThe perpendicular bisector pass through the midpoint of ABstep 1Find the midpoint AB[tex]M=((-6-2)/2,(-4+1)/2)[/tex][tex]M=(-4,-1.5)[/tex]step 2Find the slope of the given line ABThe formula to calculate the slope between two points is equal to [tex]m=\frac{y2-y1}{x2-x1}[/tex] substitute[tex]m=\frac{1+4}{-2+6}[/tex] [tex]m=\frac{5}{4}[/tex] step 3Find the slope of the perpendicular bisectorwe know thatIf two lines are perpendicular, then  the product of their slopes is equal to -1[tex]m1*m2=-1[/tex]we have[tex]m1=\frac{5}{4}[/tex]  ----> slope of the given linesubstitute in the formula[tex]\frac{5}{4}*m2=-1[/tex][tex]m2=-\frac{4}{5}=-0.8[/tex]step 4Find the equation of the perpendicular bisectorwe know thatThe equation of the line into point slope form is equal to[tex]y-y1=m(x-x1)[/tex]we have[tex]m=-0.8[/tex][tex]M=(-4,-1.5)[/tex]substitute[tex]y+1.5=-0.8(x+4)[/tex][tex]y=-0.8x-3.2-1.5[/tex][tex]y=-0.8x-4.7[/tex]