Answer:
y=5/2x-16
Step-by-step explanation:
First, we want to find the slope of the original line.
m= -4+8/-1-9
m= 4/-10
m= -2/5
Because we want the perpendicular bisector, we will need the slope to be the opposite reciprocal. Therefore, our slope is
m=5/2
Now, we want to find the midpoint of the line.
9-1/2
8/2=4
-8-4/2
-12/2= -6
So, the midpoint is (4,-6)
Using the information we have, we now can find b.
-6=5/2(4)+b
-6=10+b
-16=b
That gives us our equation
y=5/2x-16
