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Parallel And Perpendicular Lines

Learn about the relationship between parallel and perpendicular lines.

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.

Parallel And Perpendicular Lines

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.