A line passes through #(1 ,5 )# and #(8 ,7 )#. 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
MathyPerson · Stefan V.
Feb 20, 2018

#(10,8)#

Explanation:

I didn't use math to figure this out, but I'll explain both ways. First the easy way.

To get from #(1,5)# to #(3,6)#, you increase #x# by #2# and #y# by #1#, so if you do the same thing to #(8,7)#, you get #(10,8)#. If you move both points by the same amount, the slope stays the same.

Mathematically, you would have to find the slope of the line made by #(1,5)# and #(8,7)#. So you do the slope formula, and you get

#"slope" = m = (7-5)/(8-1#

which equals #2/9#. Then you use the point-slope formula and input #(3,6)# for the #x# and #y# variables and #2/9# for the #m# variable.

You end up with

#y-6=(2/7)(x-3)#

which, when you solve for #y#, becomes

#y=2/7x+36/7#

(I kept the fractions so it would be easier to solve).

Then just pick an #x# value and plug it in yo get your #y# and you're done. Yay! (You'll notice that plugging in #10# gets you #56/7#, which is #8#)

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