Answer: y = 3x-5
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Explanation:
First find the slope of the line through the two given points. Use the slope formula for this. See figure 1 in the attached images. After following those steps, the slope happens to be -1/3. From here, you flip the fraction to get -3/1 and then you flip the sign to get +3/1 or just 3/1 which is equivalent to 3. This is the slope of the perpendicular line. The slope of the answer is m = 3, which we'll use later to help determine the y intercept.
Before we can find the y intercept, we need to know what point is on this perpendicular bisector. Recall that "bisect" means to "cut in half". So we need to find the point that cuts the segment from (-3,6) to (9,2) in half. In short: we need the midpoint. Refer to figure 2 (attached image below) to see how I found the midpoint. The short version is that you add up the corresponding coordinates and then divide by 2. The midpoint found is (3,4)
Using this midpoint (x,y) = (3,4), we can find the y intercept denoted b
y = mx+b
y = 3x+b .... plug in the slope m = 3
4 = 3*(3)+b ... plug in the point (x,y) = (3,4)
4 = 9 + b
4-9 = 9+b-9 .... subtract 9 from both sides
-5 = b
b = -5
So if m = 3 is the slope and b = -5 is the y intercept, then y = mx+b turns into y = 3x-5 which is the answer we want.
