A line passes through (2 ,8 )(2,8) and ( 1, 2 )(1,2). A second line passes through ( 6, 1 )(6,1). What is one other point that the second line may pass through if it is parallel to the first line?

1 Answer
Alan P.
Apr 5, 2016

One possible point would be (12,37)(12,37)

Explanation:

A line passing though (2,8)(2,8) and (1,2)(1,2) has a slope
color(white)("XXX")m=(Delta y)/(Delta x)=(8-2)/(2-1) = 6/1=6

All parallel lines have the same slope.

So a parallel line through the point (6,1) would have the formula
color(white)("XXX")(y-1)/(x-6)=6
or
color(white)("XXX")y-1=6(x-6)

When x=12 (note that this is a completely arbitrary choice)

color(white)("XXX")y-1=6(12-6)=36

color(white)("XXX")y=37

Related questions
See all questions in Equations of Parallel and Perpendicular Lines
Impact of this question
1925 views around the world
You can reuse this answer
Creative Commons License