Learn about the relationship between parallel and perpendicular lines. After you finish this lesson, view all of our Algebra 1 lessons and practice problems.
Parallel lines have the same slope but different y-intercepts. Ex: and are parallel.
Perpendicular lines have slopes that are the negative reciprocals of each other and may or may not have the same y-intercept. Ex: and are perpendicular.
Examples of Parallel And Perpendicular Lines
Both have the same slope which is
Therefore, the lines are parallel to each other.
The slopes are negative reciprocals of each other
Therefore, the lines are perpendicular.
Let’s go over parallel and perpendicular lines.
We have two graphs each with a line.
The one on the left side has a positive slope. The line is going upwards from left to right.
If we draw a line parallel to it, it would look something like this.
If the first line is going to run over and rise at , then the second line will show the same exact rate.
So, if the slope of the first line is and the slope of the second line is , we can say that .
So if then we can say that .
Now, let’s look at the second graph.
Let’s say that this line is over and up , the slope here is .
Now if we draw a line perpendicular with this, it will look something like this.
The thing with a perpendicular line is that it goes the other way. If the first line is going up, then the perpendicular line goes down. If one line has a positive slope, then the other line has a negative slope.
Now if the first line over and up , the perpendicular line is going over and down .
So the slope of the second line is
Let’s look at these closely.
These two slopes are the negative reciprocal of each other.
Therefore, in parallel lines the slopes are equal .
While the perpendicular line is the negative reciprocal of each other.