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: $y= 2x+7$ and $y=2x-3$ 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: $y= 4x+3$ and $y=-\frac{1}{4}x+4$ are perpendicular.

Examples of Parallel And Perpendicular Lines

Example 1

$y=\dfrac{2}{3}x+5$
$y=\dfrac{2}{3}x-1$

Both have the same slope which is $\dfrac{2}{3}$

Therefore, the lines are parallel to each other.

Example 2

$y=-4x+10$
$y=\dfrac{x}{4}+\dfrac{1}{4}$

The slopes are negative reciprocals of each other

$m_1=-4$
$m_2=\dfrac{1}{4}$

Therefore, the lines are perpendicular.

Video-Lesson Transcript

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 $2$ and rise at $2$, then the second line will show the same exact rate.

So, if the slope of the first line is $m_1$ and the slope of the second line is $m_2$, we can say that $m_1 = m_2$.

So if $m_1 = 1$ then we can say that $m_2 = 1$.

Now, let’s look at the second graph.

Let’s say that this line is over $1$ and up $2$, the slope here is $m_1 = \dfrac{2}{1}$.

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 $1$ and up $2$, the perpendicular line is going over $2$ and down $1$.

So the slope of the second line is $m_2 = -\dfrac{1}{2}$

Let’s look at these closely.

$m_1 = \dfrac{2}{1}$
$m_2 = -\dfrac{1}{2}$

These two slopes are the negative reciprocal of each other.

Therefore, in parallel lines the slopes are equal $m_1 = m_2$.

While the perpendicular line is the negative reciprocal of each other.