What is the equation of the line perpendicular to #y=-3x # that passes through # (5,8) #?

1 Answer
Shwetank Mauria
Feb 20, 2016

Equation of the line perpendicular to #y=-3x# and passing trough #(5,8)# is #x-3y+19=0#.

Explanation:

The equation is equivalent to #3x+y=0# and hence equation of a line perpendicular to it will be #x-3y=k#.

This is so because for two line to be perpendicular, product of their slopes should be #-1#.

Using this it is easy to deduce that lines #Ax+By=C_1# and #Bx-Ay=C_2# (i.e.just reverse the coefficients of #x# and #y# and change sign of one of them) are perpendicular to each other.

Putting the values #(5,8)# in #x-3y=k#, we get #k=5-3*8=5-24=-19#

Hence, equation of the line perpendicular to #y=-3x# is #x-3y=-19# or #x-3y+19=0#.

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