What is the equation of the line in slope-intercept form that passes through the point (3, –5) and is perpendicular to y = –3x + 4?

1 Answer
Alan P.
Jun 30, 2016

#y=1/3x-6#

Explanation:

#y=-3x+4# has a slope of #color(purple)(-3)# (It is in slope-intercept form)
therefore
any line perpendicular to it has a slope of #-1/(color(purple)(-3))=color(green)(1/3)#

Starting with the slope-point form, with a slope of #color(green)(1/3)# and a point #(color(red)(3),color(blue)(-5))#
we have
#color(white)("XXX")y-(color(blue)(-5))=color(green)(1/3)(x-color(red)(3))#

#color(white)("XXX")y+5=color(green)(1/3)(x)-1#

#color(white)("XXX")y=color(green)(1/3)xcolor(brown)(-6)#

which is the "slope-intercept" form with slope #color(green)(1/3)# and y-intercept #color(brown)(""(-6))#

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