How to Put Perpendicular Lines Into Standard Form

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Putting perpendicular lines into standard form will require you to look at the angle between those two lines. Put perpendicular lines into standard form with help from an experienced mathematics professional in this free video clip.

Part of the Video Series: Trigonometry, Graphs, & Other Math Tips
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Hello, my name is Walter Unglaub. And this is how to put perpendicular lines into standard form. So, here I have my X, Y plane and I have two perpendicular lines, meaning that the angle between the two lines if 90 degrees. And what I can do, is write down the equation of the lines. So, for my line Y-one, I have Y-one is equal to M-one-X plus B-one. Where M-one is the slope of my first line and B-one is my Y intercept here. And for the second line, I likewise have Y-two is equal to M-two-X plus B-two. Where B-two is the value of this particular Y intercept. So, standard form means that we're going to put all of our variables on one side of the equation and all the constants on the other side of the equation. However, since these lines are perpendicular, we can write the slopes in terms of just one slope, M. Because we have the constraint that for perpendicular line,s the slope of one line times the slope of the second line, has to be equal to negative one. This means that M-one will be equal to negative one divided M-two. So, if I want to call this just simply M, then I can rewrite these in standard form in terms of just one parameter M. So, let's start with the standard form for line one. We're going to move the X term over to the left hand side. So I have negative M-one-X plus Y-one is equal to D-one. And then, for the second one, I'm going to have negative M-two-X plus Y-two is equal to B-two. So, now using this relationship, I can rewrite m-one and M-twp in terms of just M. So, for line one, I'm going to have negative M-X plus Y-one is equal to B-one. And for line two, if I substitute in M, I see that there's a relationship here. That M-two is going to be equal to negative one over M. So, I substitute this in for M-two and I get negatives canceling each other. So, I have one over M times X, plus Y-two is equal to B-two. And now, I've written the equations for two lines that perpendicular to each other in terms of the same parameter, M in standard form. My name is Walter Unglaub, and this is how to put perpendicular lines into standard form.

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