A line passes through #(3 ,6 )# and #(6 ,5 )#. A second line passes through #(4 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2016-03-21T16:05:49

#(1,4)# for instance

The slope of the first equation is
#k_1=(Delta y)/(Delta x)=(5-6)/(6-3)=-1/3#

#y-6=-1/3(x-3)# => #y=(-x+3)/3+6# => #y=(-x+21)/3#

#k_2=k_1=-1/3#

#y-3=-1/3(x-4)# => #y=(-x+4)/3+3# => #y=(-x+13)/3#

Since the equation of second line is #y=(-x+13)/3#
For instance with #x=1#
#-> y=(-1+13)/3=4#
#-> (1,4)#