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A line passes through #(3 ,2 )# and #(7 ,3 )#. A second line passes through #(1 , 4 )#. What is one other point that the second line may pass through if it is parallel to the first line?

Answer 1

Avery Allen

#(-15,0)#

Slope of line passing through say #A(3,2)# and #B(7,3)# is #(3-2)/(7-3)=1/4#

As such any line parallel to #AB# will have a slope of #1/4#.

Let us point slope form to find equation of line passing through #(1,4)# and having a slope of #1/4#, which is

#(y-4)=1/4(x-1)# or

#4(y-4)=(x-1)# or #4y-16=x-1# or

#x-4y+15=0#

One point on line #x-4y+15=0# could be, say if #y=0#, #x=-15# i.e.

#(-15,0)#

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