Answer: y = (5/2)x + 15
This is the same as y = 2.5x+10 since 5/2 = 2.5
============================================
Step-by-step explanation:
Let's find the slope of the line through those given points
m = (y2-y1)/(x2-x1)
m = (7-3)/(-9-1)
m = 4/(-10)
m = -2/5
To find the perpendicular slope, we flip the fraction and flip the sign
flip the fraction: -2/5 turns into -5/2
flip the sign: -5/2 turns into 5/2
The perpendicular slope is 5/2
Side note: The original slope (-2/5) and the perpendicular slope (5/2) multiply to -1.
-------------------------
Now find the midpoint
We add the x coordinates of the original points to get 1+(-9) = -8, which cuts in half to -8/2 = -4. This is the x coordinate of the midpoint.
Do the same for the y coordinates. First add: 3+7 = 10, then cut in half: 10/2 = 5. The y coordinate of the midpoint is 5.
The midpoint is (-4,5)
-------------------------
The perpendicular bisector will go through this midpoint. It has a slope of m = 5/2
Turn to point slope form to find the equation we need
y - y1 = m(x - x1)
y - 5 = (5/2)(x - (-4))
y - 5 = (5/2)(x + 4)
y - 5 = (5/2)x + (5/2)*4
y - 5 = (5/2)x + 10
y = (5/2)x + 10 + 5
y = (5/2)x + 15
y = 2.5x + 15 ... since 5/2 = 2.5