Answer:
y = 3x + 12
Explanation:
For the equation of the perpendicular bisector we have to first find the midpoint of the two end points.
![M(x,y)=((4+(-8))/(2),(4+8)/(2))\\\\M(x,y)=(-2,6)](https://img.qammunity.org/2021/formulas/mathematics/high-school/npbhmm5fynxh3b5dfnhvo0svwsgk3i2prt.png)
Now we need to find the slope of the line .
![m=(y_2-y_1)/(x_2-x_1)\\\\m= (8-4)/(-8-4)\\\\m=(4)/(-12) \\\\m=-1/3](https://img.qammunity.org/2021/formulas/mathematics/high-school/crm10i76a2ygxf53xu1db693nu81qri37n.png)
Now the slope of the perpendicular line is,
![m_1m_2=-1\\\\-(1)/(3)m_2=-1\\\\m_2=3](https://img.qammunity.org/2021/formulas/mathematics/high-school/5lzzprg48031p7r77hb3j20ha9s5egq9gd.png)
Now to find the equation of line , we use Point-slope form:
![y-y_1=m(x-x_1)\\y-6=3(x-(-2))\\y-6-3(x+2)\\y-6=3x+6\\y=3x+12](https://img.qammunity.org/2021/formulas/mathematics/high-school/zr9frr21u1fl5tk338zyj5cns4wrrpmslp.png)