A line passes through #(3 ,6 )# and #(4 ,7 )#. A second line passes through #(7 ,3 )#. What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
George C.
Mar 26, 2016

#(8, 4)#

Explanation:

The slope #m# of the line passing through #(x_1, y_1) = (3, 7)# and #(x_2, y_2) = (4, 7)# is given by the formula:

#m = (y_2-y_1)/(x_2-x_1) = (7-6)/(4-3) = 1/1 = 1#

So a line through #(x_0, y_0) = (7, 3)# parallel to the first line will also have slope #1#. Its equation can be written in point slope form as follows:

#y - y_0 = m(x - x_0)#

That is:

#y - 3 = 1(x - 7)#

Which we can rearrange in slope intercept form as:

#y = 1x-4#

Putting #x=8# we get: #y = 8-4 = 4#

So the second line passes through #(8, 4)#

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