# Write an equation Perpendicular to the line -3x + y = -7 and Contains the point of: (3,1)

Angel Kline 2022-10-22 Answered
Write an equation Perpendicular to the line -3x + y = -7 and Contains the point of: (3,1)
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indyterpep
Let l:−3x+y=−7, i.e., y=3x−7, be the given line, l' the
reqd. line, and the given pt. $A\left(3,1\right)\in l\prime$
Observe that the slope of l=3, &, as $l\prime \perp l,$ the slope of l' has to
be $-\frac{1}{3}$.
Further, $A\left(3,1\right)\in l\prime$
Hence, using the Slope-Point Form for l', we find,
eqn. of $l\prime :y-1=-\frac{1}{3}\left(x-3\right),i.e.,3y-3=-x+3,\phantom{\rule{1ex}{0ex}}\text{or}\phantom{\rule{1ex}{0ex}},x+3y-6=0$