 In this video, I'm going to talk about graphing using slope at a point. There are many, many methods of graphing, so this is just the first of a couple of videos I'm going to do on how to graph on a Cartesian coordinate system. You know it as just an x, y coordinate system, where you have your x's on the horizontal axis and you have your y's on the vertical axis. Okay, so for I'm just going to go over a couple of examples. Now I'm assuming a couple of things at this point. I'm assuming you know what slope is, so when we have in our directions a slope of 3 and then a point I know, I'm assuming you know what a coordinate is, an x, y coordinate. So just a couple of things that I assume that you know if you're watching this. Okay, so directions I want to graph a line that has a slope of 3 and goes through the points negative 1, 2. Okay, so just with those two pieces of information I can draw a line on my grid. Okay, so what I'm going to do is do a little bit of explaining on this on slope and on a point to help us out with this first one. So the first thing I want to do is I have a slope of 3. Slope we usually in mathematics is represented with the variable m. If you know your slope intercept form y equals mx plus b, the m portion of that is your slope. Now this is an equation we're not going to use in this video but I thought I'd point it out that's something you should memorize in your math life that's used all the time when you're graphing. But anyway, slope is usually represented with an m. So slope is normally written as rise over run. So what do we mean by rise? Rise is rising up and down on our graph and then the running portion of it is running left and running right. So that's your x-axis. So in this case we have a slope of 3. Okay, now right off the bat you should say to yourself, well that doesn't really make sense. Rise, I've got to have a number on top, run, I've got a number on bottom. Well with 3, what about a number on top, what about a number on bottom? Okay, well remember regular whole numbers like this we can make into fractions. All I have to do is write it as a 3 over 1. This is still 3. I changed what it looks like, but this number is still 3. Just like if I was to change it to 6 over 2 or if I was to change it to negative 12 over negative 4 or something like that, these two fractions, actually sorry, these three fractions are still 3. They were just written a little bit differently. If I was to simplify any one of these I'd still get back to 3. Okay, so anyway these other two fractions are not important. Get rid of them. What I want to do is I have a slope of 3, we'll just say a 3 over 1, and then I have a point, P and T is point of negative 1, 2. Negative 1, 2, where's my undo button, there it is. Negative 1, 2. All right, so the first thing I actually want to do is I want to find a point. My starting point for this is the point, negative 1, 2, a little redundancy with the words there. All right, so I'm going to start on my origin. I'm going to go to negative 1, 2, X coordinate first, so negative 1, and then 2 for the X and then the Y coordinate, so that's my starting point. All right, from there I'm going to use my slope of 3 over 1. Okay, now this is a positive slope, 3 is a positive number. So my slope is going to look something like this, so bear with me, my slope is going to look something like this, okay, that is a positive slope. Now that's not my line, I just drew an arbitrary line, that is not, this is a positive slope. I just want to draw this first. So the thing is when I do a slope of 3 over 1, I want to make sure that when I rise and run from this point, I rise up and then run to the right, or I can rise down and run to the left. Either way, I can go either way from this point, but I want to make sure that you guys know that this is in the end kind of what this line is supposed to look like because this is a positive slope, positive 3, positive slope. Okay, so let's get rid of this line here, and now let's make the actual slope of 3. So starting points at negative 1, 2, I'm going to rise 3, 1, 2, 3, and I'm going to run 1. Okay, now remember I want to run so that it's a positive slope, so that's where my point's going to be. Now notice I don't have any more room to go, what am I supposed to do now? Just go back to your original point and instead of rising up, now I'm going to rise down. Rising really doesn't mean going up, I mean you can go up or down for the rising portion of this. Okay, so I'm going to actually rise down, I'm going to fall, 1, 2, 3, and then I'm going to run 1. Now notice I ran to the left this time, that way all these points line up so that I can make a line. So let me see if I can draw this out, here we go, right there, right there, and there is my line. I have a slope of 3 and it started at this point of negative 1, 2. And that is the line, that is the line that I was going for. Okay, so that was a little bit of over explaining this next example that I do. I'm going to go a little bit faster through since we got the basics down. Okay, so another example, I'm going to do a different color here, another example. A simple line that has a slope of negative two-thirds and goes through the point four-zero. Alright, so I'm going to write this out again, slope is negative two-thirds. Two things to note here is that a negative, so it's going to go downhill this time, two-thirds, so I do have a top and a bottom, I don't have to change it like I did the three. There is a definite top and bottom, my phone's going off there. Sorry about that. Okay, so point is four-zero, okay so I'm going to start there, I'm going to start with this point first. I'm going to come to my grid, four for the X's, one, two, three, four, right there and zero for the Y's, zero for the Y means I don't go up or down, I stay right here at zero. Alright, so there's my starting point and from here now what I'm going to do is I have a negative slope, so again my line is going to look something like that, that's not the actual line again, but it's going to look something like that. So make sure when you rise and run, you go in that direction, I can either rise up and go left or I can fall down and go right, either way with a negative slope. Okay, let's get rid of that, go away, alright so I'm going to rise two, one, two, I'm going to run three, one, two, let me do that again, I'm going to rise two, one, two, I'm going to run three, one, two, three. So there's my new point right there, okay now on the previous line I actually went back to my starting point and I went the other way. So let's try that. So if I get back to my starting point, I'm going to fall two, one, two, and I'm going to run three, one, maybe two, maybe three, I don't know, I don't know where that's going to be yet. Notice that again, I go off my grid. So this isn't really a reliable point out here, so I really don't want that out there, so let's get rid of that, get rid of those marks, alright but so anyway, I don't have to come back to this starting point every time, what I can do is I can just keep going from the point that I made, so I rose one, two, ran one, two, three. So let's just do that again, I rise one, two, I run one, two, three. So there's my new point right there, alright, now again I can't rise and run anymore, so there we are, I'm stuck, this is the most I can draw on this grid anyway. So now let's just connect the dots right here, do, do, put arrows on the end of your lines of course because they're lines that go on forever and that's it. So our starting point was down here which was four, zero and there is the line that has a slope of negative two-thirds and it goes through the point four-zero. Okay, a couple of other things to note for this, that's it, that's the end of those two problems, that is enough. A couple of extras here is that when you graph these points, I would graph a minimum of 30 points, that way you can draw an accurate line, so notice what I did here, I had a point up here, for the blue line I had a point up here, point where I started at and then a point down here, so those are my three points, for the red line I started here and then I made one, I made a second point and then I made a third point here and I had my three points to make a line. Now, technically if you want to get into the definition of a line, you only need two points for a line. Okay, so technically yes, that's all you need is two points, so I could have, for my red line, I could have started with this point here, gotten my second point here then just drew my line in there, that would have been enough, but you always want to try to do a third point just to test to make sure that you did this correctly, it doesn't take very long to do an extra point and then draw a line through it, sometimes you'll get off with your point, sometimes you'll miscount, sometimes you'll make little mistakes here or there, it's always good to do a third point just to check to make sure you're doing it correctly. It saves you a lot of time, a lot of effort and you won't make many mistakes, you won't get those red marks on the paper, if you just take a little bit of extra time to draw out a couple more points. Okay, anyway, that is graphing using slope and a point, hopefully these couple of examples and my explanation of this helped you, thank you for watching.