What is the equation of the line perpendicular to #y=-3/4x # that passes through # (2,4) #?

1 Answer
Aug 23, 2017

Answer:

#y=4/3x+4/3#

Explanation:

We begin by finding the slope of the line that is perpendicular to #-3/4#. Recall that the perpendicular slope is expressed as the negative reciprocal of the slope(#m#) or #-1/m#.

Therefore, if the slope is #-3/4# the perpendicular slope is...

#-1/(-3/4)->-1*-4/3=4/3#

Now that we have the perpendicular slope, we can find the equation of the line by using the point-slope formula: #y-y_1=m(x-x_1)# where #m# is the slope and #(2,4)->(x_1,y_1)#

So to find the equation of the line...

#y-4=4/3(x-2)larr# Equation of the line

We can also rewrite the above equation in #y=mx+b# form if desired. To do this, we simply solve for #y#:

#y-4=4/3x-8/3#

#y-4=4/3x-8/3#

#ycancel(-4)cancelcolor(red)(+4)=4/3x-8/3color(red)(+4)#

#y=4/3x-8/3+[4/1(3/3)]#

#y=4/3x-8/3+12/3#

#y=4/3x+4/3#