 In this video, I'm going to talk about writing the point slope form of the equation of a line. This one is a little bit different from a previous video about writing equations. We're going to be using a different form. We're going to be using point slope form, which is written right here, y minus y1 equals m times the quantity x minus x1. Okay, now this is real confusing. This is actually something I don't use all the time. This is a handy form to use if you can get past the fact of all these y's and all these x's. If you understand what they are, then you can use this. But this is a formula that I don't really use a whole heck of a lot. But anyway, what does this all mean? So y minus y1 and then x minus x1. Notice we have an x1 and a y1. That simply just means your first x coordinate and second, excuse me, first x coordinate, first y coordinate. So that means we have to have a point. And then also in here we have an m, which is slope. So I have to know the slope of the equation. So right here, this is the point slope form. I need to know a point. I need to know the slope, and I can write the equation of a line. So that's what we're going to try to look for. So we're going to look for a point, and we're going to look for the slope to figure out what the equation of the line is. So as I look at this line, now you'll notice if you watch my previous video on slope intercept form, this is actually the exact same line. And I'm doing that on purpose to show that there are multiple ways to figure out what the equation of a line is. So there are multiple ways to do this. But what I'm going to do is I'm going to find a point that is on this line. Now if you have a picture of it visually, you can just go and just find a point. Find an intersection, find a nice, clear, clean intersection, and that's where one of your points is. So actually right here, that is one of my points. This is a different point that I used last video, but it will work nonetheless. So this is one, two, one, two. This is the point two, two. I'm not going to use that. I'm not going to use that. That point will be kind of confusing when I start plugging in numbers because it's two and two, so I'm not going to use that. Let's go find something else for the benefit of this video. Let's go find something else. Actually, let's go back to the previous point that I used actually in the last video because it actually worked quite nice. Four, three is this point. Four, three. So I'm going to use this point instead. I'm not going to use two, two because it's the same number, two and two. So when I plug it in, sometimes that confuses students and you don't know where the two came from. But in this case I have a four and a three, those are definite different numbers for what I'm going to use. So okay, here we go. Four, three. So I have a point. My point is four, three. Point is four, three. So that's the first thing I need to find. Now I need to find out what the slope is. Now there's a couple of different ways to do this. You can find another point here. So actually this two, two that I erased a second ago, that actually is going to be useful. So now what I'm going to do is I'm going to find the slope of this line using this other point. So slope is rise over run. So I'm going to rise one, run two. So my slope is one half. It's a positive one half because I'm going uphill from left to right. So positive one half. All right, those are the two things that I need to write this equation. So now what I'm going to do is I'm going to take this information and plug it in to my point slope form. Y minus your first Y coordinate, which is going to be three, equals the slope of one half times X minus X1, which my first X coordinate is four. So that's it. There you go. And then that's it. We're done. That is the point slope form of the equation. That is relatively simple. Now, as simple as that might is, and as surprised as you are, I really do not like this form of the equation because you look at this equation and you have no idea what it looks like. You look at the slope right here. So it's got a positive slope, so it goes uphill, a one half slope, so it doesn't go uphill very fast. It's not a very steep slope, but that's it. That's all you really know about this problem, about this equation. That's why I don't like using this. I would rather use slope intercept form. So let me do some math here real quick. Y minus three equals, I'm going to distribute this one half X minus two. I'm going to add three to the other side. So Y equals one half X plus one. So if you remember from the previous video, that was the equation that we got. So we can actually use point slope, and if we do a little bit of simplifying, a little bit of algebra, we can actually get the slope intercept, slope intercept form of the equation, which as you saw from the previous video is Y equals one half X plus one. Now this equation I like much better because not only do you get to see what the slope is, positive slope goes uphill left to right, one half slope, it doesn't go up very fast, but on the other hand, you can see what the Y intercept is at. So plus one right here, that's where the Y intercept is at, but you don't get to see that with this other form of the equation. You don't really get to see that. So I just wanted to show the difference between that. But anyway, answer wise, this here, point is the equation, the point slope form of the equation of the line. Okay, that's about it for that one. As long as you know a single point and the slope, then you can figure out what the equation is going to look like. And that's it. All right, that is writing the point slope form of the equation of a line. Thank you for watching, and I hope that this video was helpful.