How do you find a standard form equation for the line with (6, -1) and is perpendicular to the line whose equation is 5x + 9y - 61 = 0?

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Nam D. Share
Dec 31, 2017

Answer:

#y=9/5x-59/5#

Explanation:

First, convert #5x+9y-61=0# into #y=mx+b#

#5x+9y-61=0#

Therefore, #y=-5/9x+61/9#

The perpendicular line to #y=-5/9x+61/9# will have a slope #m=9/5#, because the product of the perpendicular line's slope and the original line's slope (#m_1m_2#) will equal #-1#.

#y_2=9/5x+c# where #c# is the y-intercept

We know that it passes through #(6,-1)#. Plug that in to #y_2#.

#-1=54/5+c#

#c=-59/5#

Therefore, the equation of the line that passes through #(6,-1)# and is perpendicular to #5x+9y-61=0# is

#y=9/5x-59/5#

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