http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
3.8 Parallel Lines in the Coordinate Plane
Here you’ll learn properties of parallel lines in the coordinate plane, and how slope can help you to determine
whether or not two lines are parallel.
What if you wanted to figure out if two lines in a shape were truly parallel? How could you do this? After completing
this Concept, you’ll be able to use slope to help you to determine whether or not lines are parallel.
Watch This
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Click image to the left for more content.CK-12 Foundation: Chapter3ParallelLinesintheCoordinatePlaneA
Watch the portion of this video that deals with Parallel Lines
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Click image to the left for more content.KhanAcademy: Equations of Parallel and Perpendicular Lines
Guidance
Recall that parallel lines are two lines that never intersect. In the coordinate plane, that would look like this:
If we take a closer look at these two lines, we see that the slopes of both are^23.
This can be generalized to any pair of parallel lines in the coordinate plane.Parallel lines have the same slope.
Example A
Find the equation of the line that is parallel toy=−^13 x+4 and passes through (9, -5).
Recall that the equation of a line in this form is called the slope-intercept form and is written asy=mx+bwherem
is the slope andbis they−intercept. Here,xandyrepresent any coordinate pair,(x,y)on the line.
We know that parallel lines have the same slope, so the line we are trying to find also hasm=−^13. Now, we need to
find they−intercept. 4 is they−intercept of the given line,not our new line. We need to plug in 9 forxand -5 fory
(this is our given coordinate pair that needs to be on the line) to solve for thenew y−intercept(b).