What is the slope of any line perpendicular to the line passing through #(-4,1)# and #(-3,7)#?

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Answer 1 · 2018-03-31T11:12:01

The slope of any line perpendicular to given line is #(-1/6)#

We know that,

#(1)# Slope of the line passing through #A(x_1,y_1)and B(x_2,y_2)# is

#m=(y_2-y_1)/(x_2-x_1)#

#(2)# If the slope of the line #l_1# is #m_1and# the slope of
the line #l_2# is #m_2# then

#l_1_|_l_2 <=>m_1m_2=-1#

We have line #l_1# passing through #A(-4,1)andB(-3,7)#.

Using #(1)# we get

#m_1=(7-1)/(-3+4)=6#

Now from #(2)#,we have

#m_1m_2=-1#

#=>(6)m_2=-1#

#=>m_2=-1/6#

#:.#The slope of any line perpendicular to given line is #(-1/6)#