How do you find the slope that is perpendicular to the line #y=(-3x)#?

1 Answer
Jul 18, 2016

Answer:

Slope of the perpendicular: #color(green)(1/3)#

Explanation:

The standard general form of a linear equation in slope-intercept form is:
#color(white)("XXX")y=color(green)(m)x+color(blue)(b)#
with slope #color(green)(m)# and y-intercept #color(blue)(b)#.

The given equation #y=(-3x)#
can be re-written to be in explicit slope-intercept form as:
#color(white)("XXX")y=color(green)(""(-3))x+color(blue)(0)#
with slope #color(green)(""(-3))#

If a line has a slope of #color(m)#
then all lines perpendicular to it have a slope of #color(green)(""(-1/m))#

Since #y=-3x# has a slope of #color(green)(m=-3)#
any line perpendicular to it will have a slope of
#color(white)("XXX")color(green)((-1/m)=-(1/(-3))=1/3#