 In this video I'm going to talk about graphing using intercepts out of all the ways to graph. This is actually my least favorite method of graphing but a lot of students actually prefer this method of graphing because it's a little bit more visual and there's a little bit of arithmetic involved in this and some students like to do all that arithmetic. I don't necessarily need to. I think there's a better way to do this but anyway this is one way of doing this. This also helps us to understand what an x-intercept and what a y-intercept is. So that actually is a good part of what we're doing here. Okay so anyway we're going to graph using intercepts. So that's actually we're going to figure out this equation here. We're going to figure out where it hits the y-axis and then we're also going to figure out where it hits the x-axis on a grid and so with those two points if we graph those two points then we'll be able to graph wherever the line is supposed to be. Okay so and normally some equations are written this way. Notice that the x and the y are on the left side of the equal sign. Notice that both of them are on the left. That is traditionally what we call the standard form of an equation where we have all the variables on the left side and then the numbers on the right. So you see the x variable and then the y variable on the left and then the number on the right. That's traditionally how we see it. Okay so if you have an equation in this form we can find the intercepts. Now to find the intercepts there's two things you got to do. We got to find the x intercept and we got to find the y intercept. So I'm going to show finding the x intercept first. Okay so x int that's x intercept. I'm going to do that first. Now to do this to find the x intercept this is kind of counter intuitive. What we're going to do is we're going to assume that y is equal to zero. Again a little counter intuitive. To find the x intercept we want to see when the y is zero. We want to assume the y coordinate is zero. So what we're going to do is we're going to take this equation and we're going to plug in that y is equal to zero into this equation. So it's going to look like this. 4x minus 2 times zero equals 8. So now all we're doing is we're just plugging in and now what we're going to do is since we only have one variable left we just have this x variable left. We're going to solve for that x variable. Okay now I know some of you think at all solving I got to do algebra, I got to do all this extra work. It's not really actually that complicated. You should love working with zero because notice what happens right here. Negative 2 times zero that is zero that simply just goes away all I'm left with is 4x is equal to 8. Then all I need to do is divide by 4 on both sides and then x is equal to 2. So actually it doesn't take very much to find out what that what the excuse me x intercept is going to be. Now what am I supposed to do with this? The intercepts are supposed to be coordinates. I'm supposed to have an x-coordinate then a y-coordinate. This is only one number so what's this mean? Okay there's two ways to look at this. The first way which I actually don't use but some students do. Since this is an x-intercept they just go with the vocabulary x-intercept. That's where it hits the x-axis. So I'm going to take this number this is where it hits the x-axis and bring that number to the x-axis that number was 2 so it's right here. That's one way to look at it that's one way to see where the x-intercept is at. The other way to see it and this is what I do. I know that the y is zero that's one thing I assumed y is zero and then the x is two that actually gives you a coordinate of two zero. With the coordinate x2 y is zero I come back to my origin and x is two and a y is zero. It's the exact same point. So again two different ways to see where that point is supposed to be. I just want to show you both ways because again students prefer one thing or the other. All right so that is how to find the x-intercept. Now let's look at finding the y-intercept. So y-intercepts again int stands for intercept. So as you can well imagine I'm going to go a little bit faster through this is that for the x-intercept I assume that y was equal to zero. You can kind of assume that we're going to do the same over here. For the y-intercept I'm going to assume that the x is equal to zero. So we kind of switch it up depending on which one we're trying to find. So now we're going to use the same equation again. So four times zero make sure you put the x equals zero make sure you put in the right spot minus 2y equals eight. We don't want to do this equation all over again. And again love working with zero because everything goes away. So four times zero is zero so that goes away. So I'm left with 2y on that left side and then all I need to do is divide by negative two and that gives me a negative four. So divided by negative two here they'll cancel and then eight divided by negative two is negative four. So again here two ways of thinking y equals negative four. This is a y-intercept so I can go to the y-axis and look for negative four which is all the way down here. That's one way to think of it. Or my preferred way is that I look at here's a y of negative four there's an x of zero so zero negative four is my point. So an x of zero okay don't go left or right and then a y of negative four which is this point right down here. So again the same point two different ways to look at it but it's the same point. Alright so that is my that's how I find the x-intercept and the y-intercept and now that I have those two points now what I can do is I can draw a line between them. So I'm going to use green to do the line between them. So I'll start I'll start somewhere down here and there we go. Okay I didn't quite perfectly go through there but I have my two points they're easily visible and there's my line. And that's it that is graphing using intercepts. It's pretty simple but you got to make sure that you understand the steps. The most difficult thing I think about this is that when you have an x-intercept you make the y equal to zero and then you solve to get a point and then it's opposite when you want a y-intercept set the x equal to zero plug it in solve it and you get your other coordinate. There's a little bit of algebra involved with this method so that's why sometimes it's not popular with students but it's still a good method to use because you can see where the x-intercept is you can see where the y-intercept is. And depending on whether this is a word problem or not that x and y-intercept usually tells you something about the story sometimes it'll tell you where you started at sometimes it'll tell you where you end at again depends on the word problem. But anyway make sure that when you are using when you're using intercepts when you have an equation that looks like this these are the these are the two things you look for find the x-intercept find the y-intercept and this is the way to do that. Alright and that is graphing lines using intercepts thank you for watching the video