A line passes through #(3 ,9 )# and #(5 ,1 )#. A second line passes through #(7 ,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
Sep 22, 2016

Any point other than #(7,6)# and satisfying the condition #4x+y=34# could be such a point. Examples are #(0,34)#, #(-8,66)# and #(12,-14)#.

Explanation:

A line passing through #(x_1, y_1)# and #(x_2, y_2)# has a slope of #(y_2-y_1)/(x_2-x_1)#. Hence slope of line joining #(3,9)# and #(5,1)# is

#(1-9)/(5-3)=-8/2=-4#

As the second line passing through #(7,6)# is parallel to the above, its slope too is #-4#.

Now, equation of a line passing through #(x_1,y_1)# and having a slope of #m# is #(y-y_1)=m(x-x_1)#. Hence, the equation of line passing through #(7,6)# and having a slope of #-4# is

#(y-6)=-4(x-7)# or #y-6=-4x+28# i.e. #4x+y=34#

Hence, any point satisfying the condition #4x+y=34# (other than #(7,6)# will satisfy this.

Let #x=0# then #y=34#, hence point could be #(0,34)# or

let #x=-8# then #y=66#, hence other point could be #(-8,66)# or

let #x=12# then #y=-14#, hence point could be #(12,-14)#

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