What is the equation of the line that passes through #(-1,3)# and is perpendicular to the line that passes through the following points: #(6,-4),(5,2)#?

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Answer 1 · 2016-01-06T16:51:52

Final answer: #6y=x+19# oe.

Defining line that passes through #a:(-1, 3)# as #l_1#.
Defining line that passes through #b:(6, -4), c:(5, 2)# as #l_2#.

Find the gradient of #l_2#.
#m_2=(y_b-y_c)/(x_b-x_c)=(-4-2)/(6-5)=-6#

#l_2_|_l_1#

So #m_1=-1/m_2=-1/-6=1/6#

Equation of #l_1#:
#y-y_a=m_1(x-x_a)#

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

#6y-18=x+1#

#6y=x+19#

Or however you want it arranged.