CK-12 Geometry Concepts

3.8. Parallel Lines in the Coordinate Plane http://www.ck12.org

− 5 =−

1

3

( 9 )+b

− 5 =− 3 +b Therefore, the equation of line isy=−

1

3

x− 2.

− 2 =b

Example B

Which of the following pairs of lines are parallel?

• y=− 2 x+3 andy=^12 x+ 3


• y= 4 x−2 andy= 4 x+ 5


• y=−x+5 andy=x+ 1

Because all the equations are iny=mx+bform, you can easily compare the slopes by looking at the values ofm.
To be parallel, the lines must have equal values form. Thesecondpair of lines is the only one that is parallel.

Example C

Find the equation of the line that is parallel to the line through the point marked with a blue dot.

First, notice that the equation of the line isy= 2 x+6 and the point is (2, -2). The parallel would have the same slope
and pass through (2, -2).

y= 2 x+b

− 2 = 2 ( 2 )+b

− 2 = 4 +b

− 6 =b

The equation of the parallel line isy= 2 x+−6.

Watch this video for help with the Examples above.

MEDIA

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CK-12 Foundation: Chapter3ParallelLinesintheCoordinatePlaneB

Vocabulary

Two lines in the coordinate plane with the same slope areparalleland never intersect.Slopemeasures the steepness
of a line.