A line passes through #(5 ,8 )# and #(7 ,9 )#. 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?

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Answer 1 · 2016-09-11T10:36:59

For 2 lines to be parallel, they need to have the same slope

Get the slope of the first line

#m = (y_1 - y_2)/(x_1 - x_2}#

#m = (8 - 9)/(5 - 7)#

#=> m = 1/2#

Now get the equation of the 2nd line

#y = mx + b#

#6 = (1/2)3 + b#

#=> 12 = 3 + 2b#

#b = 9/2#

Hence, the equation of the 2nd line is

#y = 1/2x + 9/2#

To find another point that the line passes through, simply substitute any value of #x# (or #y#) and solve for the value of the other