 In this video I'm going to talk about writing the slope intercept form, I go up to my little title here, writing the slope intercept form of the equation of a line. So this is going to be a video where we look at the picture, so notice I have a picture, I have a line right here, we're going to take this line and we're going to write the equation for it. So this is a little bit different from what we're used to, usually we have the equation of a line and we try to draw the picture. Now opposite, we have the picture of the line and now we want to do is write the equation for it. Okay, so the first thing that we want to do is when we're looking at this line is we want to decide which form, what we want it to look like. So in this case we want to have our equation in slope intercept form. So what I have right here in text is slope intercept form. So y equals mx plus b, m is slope, b is y intercept. Alright so now what I have to do to write an equation in slope intercept form, there's two things I need to know. I need to know what the slope is and I need to know what the y intercept is. That's only two things that I need to know. The x and the y, we won't really plug in anything for those. We won't really plug in anything for them. Alright so there's a couple different ways that we can do this. I'm actually going to show two ways of doing this. I'm going to show both ways of doing this because it can be a little bit tedious of which one I'm supposed to use, things like that. I'm going to do the easy version first and then a little bit tougher version right afterwards. Okay, but still the only two things that I need are the slope here and the y intercept here. So let's go to the picture and try to find those. So slope, slope, slope, slope. How much am I rising and running to get from point to point on the line? So to find out what the slope is, what I have to do is I have to find points on this line. Now a good thing to use is to use the grid that's in the background. Use the grid in the background and find out what these points are where it intersects one of the corners. So right here, that right there, that is a definite point that you can figure out. That point right there is four three, four three. Now to find out what the slope is, all I need to know is two points. Just like when you create a line, when you want to draw a line, the only thing you need to have is two points. When I want to write the equation for a line, the only thing I need is two points. So now what I want to do is I want to go down my line and I want to find another point. Now it doesn't matter where that point's at, it doesn't matter at all. So what I'm going to do is actually I'm going to go right here, this right here, that is a point that intersects right with the y axis and then this line right here. So right there, that's another point that I want to use. Now y specifically that point, well because it hits the y axis, that's a y intercept. I know exactly what that is and that's going to help me to write my equation over here. This is the point zero one, that's the point zero one. All right, so what I need to do now is I need to use, I need to find out a little bit more information and try to write the equation for this line. Actually with the information that I have, I can actually, I actually have a little bit of information, I have half the information that I need. Right here, this point, that is the y intercept for this line. This is the y intercept, that's one of the things I need right over here. B, that is my y intercept. So I actually know what this portion is out here. So if I look over here, my y intercept is one right here, plus one, it's a positive one. So actually I'm halfway done. I have found out what the y intercept is. Now I just need to find out what the slope is. Now I just gotta figure out what the slope is. Yeah, that's what's gonna go on that blank spot right there. To figure out what slope is, we have to remember back to what the definition of slope is. Slope is the rise and the run of an equation. So since I have my two points, I'm going to rise and run to get from point to point. So in this case, I would rise, I can start here. So rise two, and then run one, two, three, four. So I'm gonna rise to run four. So my slope is two over four, which is going to reduce to one half. Now I wrote it over here because I knew that it was going to reduce. I just didn't want to plug it into the equation as two over four. That doesn't make any sense. All of our fractions we want to reduce to lowest terms. So this is gonna be one half is our slope, okay? Now, before you think you're done, one thing we always have to take into account. Slope is positive or negative. In this case, my slope is going uphill from left to right, uphill from left to right. So that means my slope is positive. So that means I don't actually have to change anything here. I have a positive one half for my slope. So that's it. That is the equation of that line, okay? So that's the first method of doing this. The second method is a little bit tougher, but the second method involves not actually knowing what the, excuse me, not actually knowing what the y-intercept is going to be. So this is what I'm gonna do. I'm going to erase a little bit, okay? I'm gonna erase this. I don't want to erase too much because I don't want to erase my line. But I am going to assume for a moment, okay? So this is my first problem, okay? This is my first problem. Let's just leave it there. I want to erase it. Okay, I'm going to assume that I didn't find this point. I'm going to assume that I don't know what the y-intercept is and I can't find it, okay? So what I'm gonna do is I'm actually going to find a different point on this line. So as I look at all the different intersections that I see here, one of them that I see is right down here, right down here, okay? What is the point negative 2, 0, okay? So again, this is the second way of doing this. We already know what the answer is. I understand that. But now what we're doing is I'm showing you a different way of doing this, a different way of doing this. All right, so I'm gonna make my second problem down here, y equals mx plus b. So again, the two things that I want to find, the two things that I want to find is I want to find the slope and I want to find the y-intercept. Those are the two things that I want to find. So I'm gonna use my information here to find the slope and the y-intercept. Okay, so now the thing is is I can actually figure out what the slope is. That's not that big of a deal. I'm gonna do the same thing I did last time. I'm going to use the rise and the run, or actually, excuse me, I could use the rise and the run. I'm gonna show you a different way of figuring out how to find slope, okay? In your studies of mathematics, one of the things you have figured, you have come across is what's called slope formula. Slope formula is m equals the difference in the y's, y1 minus y2 over the difference in the x's, x1 minus x2, okay? This right here is your slope formula. We're going to use that to figure out what slope is. Okay, a little bit different from the previous method. All right, so what I'm gonna do is I'm gonna take the y's and I'm going to subtract them. So now I need to go up to my points. Here are my points, negative 2, 0, and 4, 3. Those are my two points. I'm gonna find the y's. I have a y of 0, okay, so that's my first one I put in there. I have a y of 0 and I have a y of 3, and I'm going to subtract those. So I'm gonna subtract the y's and I'm also going to subtract the x's. I gotta come over here. I have an x of negative 2 minus an x of 4. Oh, what am I doing? I was thinking too much about x's and an x of 4. So take your y's, subtract them. Take your x's, subtract them. Negative 3, 0 minus 3 is negative 3. Negative 2 and negative 4 make negative 6. This actually reduces to 1 half. Now we knew what the slope was gonna be. We already know what the slope was gonna be from the previous way of doing this problem. I just wanted to show you that we can also use slope formula to figure out what the slope is, a slope of 1 half. So that is actually part of my equation, y equals 1 half x plus whatever the y-intercept is. Now in this case, I don't know what the y-intercept is. I wasn't able to find it, wink, wink, say that I wasn't given this point or it was hard to see what this point was. I don't actually know this point right here. So what do I do? The next thing that I do is actually this x-piece and this y-piece, I actually do know something about that. Notice here I have an x, y coordinate of 4, 3 and I have an x, y coordinate of negative 2, 0. I can actually use either one of these points and I'm going to plug them in to this part of the equation to figure out what b is. So I'm actually, to make things simple for myself, I'm going to use 4, 3. So I have a y of 3 and an x of 4. So notice what I do, I'm just using a little bit of algebra. I am plugging in everything that I know. I knew a y, I knew the slope, I knew the x, I plugged them all in. I don't know what the b is, but that's okay, it's the only variable left over. I can solve for this one variable. If I solve for b, I solve for the y-intercept and I can finally write the equation of this line. All right, so this is going to be 3 equals half of 4 is 2 plus b, I run out of room down here. So over here, what I'm going to do is I'm going to subtract 2 to the other side. So 3 minus 2 is 1. So I know that my y-intercept is 1. And again, we already knew that, we already knew that from the last way of doing the problem, but again I wanted to show you a different way of doing this. So these are the two things that I needed, I needed my slope and I needed a y-intercept. So I can now write the equation y equals 1 half x plus 1. That is a different way of doing it, but again this emphasizes that the only two things that I need is I need to know what the slope is and I need to know what the y-intercept is. Once I know those two things, then I can write the equation of the line. And what I did there is I just showed you kind of two ways of using it. There's a lot you can do by just drawing a picture and rising and running and seeing that. You can also do this, you can also find slope with a formula, with slope formula. So again, a couple different ways to do this, but the one thing I want to leave you with is that when you are writing the slope-intercept form of an equation of a line, the only two things that you need are the slope and the y-intercept. Once you figure those two things out, then you can write the equation. Find the slope, find the y-intercept, then you can write the equation. Okay, hopefully this video was informative, hopefully this will help you. Thanks for watching.