How do I write the equation of a line that is perpendicular to #y=3x+4# and goes through the point (3,5)?

1 Answer
Nov 21, 2015

#y=-1/3x+6#

Explanation:

Two perpendicular lines have opposite reciprocal slopes.

The slope in #y=3x+4# is #3#, so the line perpendicular to it will have a slope of #-1/3#.

We can write this in the form #y=-1/3x+b# and then plug in #(3,5)# for #x# and #y# to find the equation of the line perpendicular to the line #y=3x+4# that goes through the point #(3,5)#.

#5=-1/3(3)+b#
#5=-1+b#
#6=b#

Therefore, the equation of our new line is: #y=-1/3x+6#.