How do you write an equation of a line, given #(4,5)# that is perpendicular to the line #3x-4y=7#?

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Answer 1 · 2017-06-30T19:30:05

#4x +3y=31#

Rearrange the original equation into form: #y=mx+c#

# (y=3/4x-7/4).#

The perpendicular gradient is the negative reciprocal of #3/4 #
(just change the sign and flip the fraction upside down)
which is # -4/3#.

Now use # y-y_1=m(x-x_1) ,# substituting the #4 and 5#.

#y -5 = -4/3(x-4)#

Rearrange the resulting equation (usually asked for in integer form)

#y -5 = -4/3x+16/3" "xx3#

#3y-15 = -4x +16#

#4x +3y = 31#