A line passes through #(2 ,9 )# and #(5 ,6 )#. A second line passes through #(3 ,8 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Alan P.
May 14, 2016

#(1,10)# would be one possible other point

Explanation:

The line through #(2,9)# and #(5,6)# has a slope of
#color(white)("XXX")m=(9-6)/(2-5) = -1#
or expressed in another way the slope ratio is
#color(white)("XXX")Deltay:Deltax=-1:1#

Any parallel line will also have this same slope ratio.

If a line passes through #(3,8)# with a slope ratio of #-1:1#
then points on the line will have the form: #(3+k,8-k)# for a constant #k#.

Picking an arbitrary value of #k#
#color(white)("XXX")k=-2#
would give the point #(3-2,8-(-2))=(1,10)#

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