Answer:
y = 3x + 12
Step-by-step explanation:
For the equation of the perpendicular bisector we have to first find the midpoint of the two end points.
[tex]M(x,y)=(\frac{4+(-8)}{2},\frac{4+8}{2})\\\\M(x,y)=(-2,6)[/tex]
Now we need to find the slope of the line .
[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m= \frac{8-4}{-8-4}\\\\m=\frac{4}{-12} \\\\m=-1/3[/tex]
Now the slope of the perpendicular line is,
[tex]m_1m_2=-1\\\\-\frac{1}{3}m_2=-1\\\\m_2=3[/tex]
Now to find the equation of line , we use Point-slope form:
[tex]y-y_1=m(x-x_1)\\y-6=3(x-(-2))\\y-6-3(x+2)\\y-6=3x+6\\y=3x+12[/tex]
