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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

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 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.