Learn about the relationship between parallel and perpendicular lines.
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.
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.