Answer:
[tex]y=-0.8x-4.7[/tex]
Step-by-step explanation:
Let
[tex]A(-6,-4), B(-2,1)[/tex]
we know that
The perpendicular bisector pass through the midpoint of AB
step 1
Find the midpoint AB
[tex]M=((-6-2)/2,(-4+1)/2)[/tex]
[tex]M=(-4,-1.5)[/tex]
step 2
Find the slope of the given line AB
The 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 3
Find the slope of the perpendicular bisector
we know that
If 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 line
substitute in the formula
[tex]\frac{5}{4}*m2=-1[/tex]
[tex]m2=-\frac{4}{5}=-0.8[/tex]
step 4
Find the equation of the perpendicular bisector
we know that
The 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]
