A line passes through #(4 ,3 )# and #(2 ,9 )#. A second line passes through #(7 ,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 · 2018-06-23T06:20:28

#color(maroon)("One other point on the second line is " (6,9)#

#"Slope of line 1 " = m = (y_2 - y_1) / (x_2 - x_1) = (9-3) / (2-4) = -3#

![https://math.tutorvista.com/geometry/http://distance-between-lines.html](https://useruploads.socratic.org/QH6H3aLYSWuXO6pacjwH_parallel-lines.png)

As #2^(nd)# line is parallel to the first line, slope of second line also #-3#

#"Equation of second line in point - slope form is "

#(y - 6) = -3 * (x - 7)#

#3x + y = 27#

Let y = 9. Then x = 6#

#color(maroon)("One other point on the second line is " (6,9)#