Answer:
[tex]y=2x-2[/tex]
Step-by-step explanation:
First, lets find the mid-point between those two points:
[tex](\frac{-1+7}{2},\frac{6+2}{2})\\=(3,4)[/tex]
Now, lets find the gradient of the perpendicular bisector:
[tex]-1\times(\frac{6-2}{-1-7})^{-1}\\=-1\times\frac{-8}{4}\\=2[/tex]
Next, we can find the equation:
[tex]y=2x+c\\4=2\times3+c\\c=4-6\\c=-2\\\Rightarrow y=2x-2[/tex]
