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whats an equation perpendicular to x+y=6 and passes through (2, 8)

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Re-working the equation by subtracting x from both sides gives:
y = -x + 6  With a slope of -1
Perpendicular slopes are the negative reciprocal of the initial slope
y = x + k is our new equation, with some displacement "k"
Using point slope formula,  y-y= m(x-x1)
y - 8 = 1*(x-2)
Add 8 to both sides and distribute the right side
y = x + 6 , or   -x + y = 6


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