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?

Question

1390 views around the world

You can reuse this answer
Creative Commons License

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