A line passes through #(4 ,9 )# and #(2 ,7 )#. A second line passes through #(2 ,6 )#. What is one other point that the second line may pass through if it is parallel to the first line?

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Answer 1 · 2016-03-31T13:45:28

Parallel means the slope is equal. Therefore we must find the slope of the first two points.

The formula for slope is #m = (y_2 - y_1)/(x_2 - x_1)#

#m = (7 - 9)/(2 - 4)#

#m = -2/-2#

#m = 1#

Now, we use point slope form to insert the other point.

#y - y_1 = m(x - x_1)#

#y - 6 = 1(x - 2)#

#y - 6 = x - 2#

#y = x + 4#

Any two points #{x, y}# satisfy this equation are on your desired line. For example, (-3, 1) is a point on this line.

Hopefully this helps!