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

1 Answer
Shwetank Mauria
May 15, 2016

Any point lying on #2x+y=12#, will satisfy this condition. One such point is #(-9,30)#

Explanation:

The slope of line passing through #(x_1,y_1)# and #(x_2,y_2)# is given by #(y_2-y_1)/(x_2-x_1)#,

Hence slope of line joining #(5,9)# and #(8,3)# is #(3-9)/(8-5)=-6/3=-2#

Slope of a line parallel to this line will also be #-2# and using point slope form of equation the equation of line passing through #(3,6)# and a slope of #-2# is

#(y-6)=(-2)*(x-3)# or #y-6=-2x+6# or #2x+y=12#

Hence any point lying on #2x+y=12#, will satisfy this condition.

Let us put #x=-9# then #-18+y=12# or #y=30#

Hence one such point is #(-9,30)#

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