How do you write an equation of a line perpendicular to #y=1/4x+2# and passes through (0,0)?

1 Answer
Nov 11, 2016

Answer:

#color(green)(y=-4x)#

Explanation:

The given equation : #y=color(red)(1/4)x+color(blue)2#
is in slope-intercept form with slope #color(red)(1/4)#

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

Therefore any line perpendicular to the given line must have a slope of #color(magenta)(-4)#
and since the requested line is to pass through #(0,0)# (which implies a y-intercept of #color(blue)(0)#
in slope-intercept form this line must have an equation:
#color(white)("XXX")y=color(magenta)(-4)x+color(blue)0#
or just
#color(white)("XXX")y=color(magenta)(-4)x#