Answer: y = -2
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Explanation:
Find the slope of line m using the slope formula
slopeM = (y2-y1)/(x2-x1)
slopeM = (2-8)/(-1-6)
slopeM = -6/(-7)
slopeM = 6/7
The slope of line m is 6/7. The perpendicular slope is -7/6. We flip the fraction (aka reciprocal) and flip the sign (from positive to negative). The phrase "flip the fraction and flip the sign" is a handy way to think of "negative reciprocal", at least in my opinion. Note how the two slopes 6/7 and -7/6 multiply to -1 to prove they are perpendicular slopes
We'll use the slope formula again to set up the slope for line n. We don't know y, but we can set the fraction equal to -7/6 and solve for it.
slopeN = (y2-y1)/(x2-x1)
slopeN = (y-5)/(5-(-1))
slopeN = (y-5)/(6)
-7/6 = (y-5)/6
-7*6 = 6(y-5)
-42 = 6y-30
6y-30 = -42
6y = -42+30
6y = -12
y = -2
So in short, if y = -2, then line n goes through (-1,5) and (5,y) = (5,-2). The slope of line N is computed to be...
slopeN = (y2-y1)/(x2-x1)
slopeN = (-2-5)/(5-(-1))
slopeN = (-2-5)/(5+1)
slopeN = -7/6
which is the proper slope value we want.
