A line passes through #(9 ,5 )# and #(6 ,8 )#. A second line passes through #(7 ,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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1 Answer
Alan P.
Mar 31, 2016

#(color(green)(0,10))#

Explanation:

A line passing through #(9,5)# and #(6,8)# has a slope of
#color(white)("XXX")m=(Delta y)/(Delta x) = (8-5)/(6-9)=3/(-3) =-1#

All parallel lines have the same slope.

So a parallel line passing through #(7,3)# and some other point #(x,y)# will have the form:
#color(white)("XXX")(y-3)/(x-7)=-1#
or
#color(white)("XXX")y=10-x#

Picking an arbitrary value for #x#, say #x=0#
we have
#color(white)("XXX")y=10# as a corresponding point.

So one point that satisfies the given requirements is #(0,10)#

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