How do you find the slope of a line perpendicular to #3x+y=15#?

1 Answer
Jun 17, 2015

Answer:

Subtracting #3x# from both sides you get: #y = -3x+15#, which is in standard slope-intercept form, with slope #m = -3#.

Any line perpendicular to it will have slope #-1/m = 1/3#

Explanation:

Either just use the answer above, asserting the #-1/m# formula, or show it geometrically as follows:

Starting with #3x+y=15#, first reflect the line in the #45^o# line #x=y#, by swapping #x# and #y#...

#3y+x=15#

Then reflect in the #y# axis by reversing the sign of #x#

#3y-x=15#

These two geometric steps are equivalent to rotating by a right angle centred on the origin.

Next add #x# to both sides to get:

#3y = x + 15#

Finally divide both sides by #3# to get:

#y = 1/3x + 5#

This is in slope-intercept format with slope #1/3#