http://www.ck12.org Chapter 3. Parallel and Perpendicular Lines
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).
− 5 =−
1
3
( 9 )+b− 5 =− 3 +b Therefore, the equation of line isy=−1
3
x− 2.
− 2 =bExample 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.