What is the equation of the line that is perpendicular to the line #-3x + y = -2# and contains the point (3,6)?

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Answer 1 · 2017-09-20T04:42:12

#3y + x = 21#

Use

#y = m x + c#

where #m# is the slope

#-3x + y = -2#

#y = 3y - 2#

So

#m = 3#

The slope of the perpendicular line is #-1/3# as

#m_1 * m_2 = -1#

The equation of the perpendicular line is

#(y-y_1) = m_2(x-x_1)#

where #m_2# is the slope of the perpendicular line #= -1/3# and #x_1# and #y_1# are the #x# and #y# coordinates of a point on it.

#y-6 = -1/3 *(x-3)#

#3y-18 = -x+3#

#3y+x = 21#

is the equation of the perpendicular line.