A line passes through #(5 ,8 )# and #(2 ,2 )#. A second line passes through #(1 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Alan P.
Jun 1, 2016

#(0,1)# is one possible point on the second line

Explanation:

If a line #L_1# passes through #(5,8)# and #(2,2)#
it has a slope #m_1= (Deltay)/(Deltax)=(8-2)/(5-2)=2#

If #L_2# is parallel to #L_1# it must have the same slope
#color(white)("XXX")m_2=2#

If #L_2# passes through #(1,3)# and has a slope of #m_2=2#
its equation can be written in slope point form as
#color(white)("XXX")(y-3)=2(x-1)#
or, more concisely as
#color(white)("XXX")y=2x+1#

Setting #x=0# (for example) gives #y=1#
so #(0,1)# would be another point on the second line #l_2#

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