http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
- 2x− 3 y=6 and 3x+ 2 y= 6
- 5x+ 2 y=−4 and 5x+ 2 y= 8
- x− 3 y=−3 andx+ 3 y= 9
- x+y=6 and 4x+ 4 y=− 16
- Find the equation of the line that is parallel toy=^14 x+3 and passes through (8, -7).
- Find the equation of the lines below and determine if they are parallel.
Answers:
- First change all equations intoy=mx+bform so that you can easily compare the slopes by looking at the values
ofm. Thethirdandfifthpair of lines are the only ones that are parallel. - We know that parallel lines have the same slope, so the line will have a slope of^14. Now, we need to find the
y−intercept. Plug in 8 forxand -7 foryto solve for thenew y−intercept(b).
− 7 =
1
4
( 8 )+b
− 7 = 2 +b
− 9 =bThe equation of the parallel line isy=^14 x−9.
- The top line has ay−intercept of 1. From there, use “rise over run” to find the slope. From they−intercept, if
you go up 1 and over 2, you hit the line again,m=^12. The equation isy=^12 x+1.
For the second line, they−intercept is -3. The “rise” is 1 and the “run” is 2 making the slope^12. The equation of this
line isy=^12 x−3.
The lines areparallelbecause they have the same slope.
Interactive Practice