 Okay, this will be my final video on instructing how to graph. This is graphing vertical and horizontal lines. This is actually as simple as the equations look. This is actually pretty tricky to remember how to graph vertical and horizontal lines. Okay, now, what am I talking about? If you look down here, y equals negative 3 and x equals 1 half, 1.5. Okay, those are the equations. That's it. That's all there is to them. Now, as simple as those look, yes, those can be kind of deceiving to whether they're vertical or horizontal lines. So we're going to go over which is horizontal, which is vertical, and all that kind of good stuff. Now, traditionally, when you see an equation, you'll see something to the effect of negative 3x plus y equals 5. That's a linear equation that you could graph. You could also see y equals 5x minus 12. That is also another equation that you could graph. This equation is in standard form, and then this equation down here is in slope-intercept form. You can graph either one of those, but that's what we're used to seeing for graphing equations. These over here are too simple. This one only has a y, this one only has an x, and so it's sometimes a little bit confusing which ones are horizontal, which ones are vertical, and if you could even graph them as lines. But there's a little bit of contrast between the two. What you're used to seeing, and then what we're going to see in this video. To get started, reading directions. We are graphing vertical and horizontal lines. First thing, we're determined if each line is vertical or horizontal, and then we are supposed to graph it. Vertical lines, vertical go up and down. So vertical go up and down and horizontal, horizontal horizon goes left and goes right. Vertical and horizontal, that's kind of what they look like just to go over the vocabulary real quick. What we want to do is identify which one is which, are they horizontal, are they vertical, and then we want to put them on the x, y coordinate grid over here. First thing, first one is y is equal to negative three. Some students make the mistake of thinking that that's just a point. No, it's not necessarily a point if we are asked to make it a line, if we're asked to make it a line. Then we have to think of it as a line, we can't think of it as just a single point anymore. But if you think of it as a single point, that can actually help you out a little bit. That can actually help you out a little bit. So actually what I'm going to do first is I'm not going to determine if it's horizontal or vertical. I'm not going to kind of do that first. What I'm actually going to do is I'm going to go to the grid first. So I'm going to identify where this is at, y equals negative three. Y equals negative three. So I'm going to go to the y-axis since it's y equals negative three and I'm going to go to exactly that point on the axis, y equals negative three. So right about here. That right there, that gives you a starting point. It gives you a starting point of where I'm going to start to create my line. All the other videos that I've done for graphing lines is that you have to have one starting point and then from there you can either create more points or you can create a line or something to that effect. We're always going to have a starting point. So for this line, I'm going to start at this point all the way over here. Now we need to determine, that's a starting point. Now we need to determine if it's going to be horizontal or if it's going to be vertical. Now you can either just memorize which one's a horizontal, which one's a vertical, or if you're like me, I couldn't memorize it so I had to just logically think about it. Now I want to create a line, I want to create a line that's y equals negative three. Now what does that actually mean, y equals negative three? Well if we look at the grid, if we look at the y axis, the y axis is your up and your down, up and down. So I want to create a line that always has an up and down of three. It always has the height, excuse me, of negative three. So I can look at my different lines, so I can look at my vertical, I can look at my horizontal. So let's go to the vertical first since this is the first on my list. So let's go to vertical. It's kind of hard to see since it's right on the y axis, but there we go. Now let's look at that, I'm not guaranteeing to say that's right, but let's just look at it. Let's think about it. That right there, does that line y equals negative three, does that always have a height of negative three? Hmm, let's think about this. Well as I go up and down this line, I'm going to hit a y of negative four. I'm going to hit a y of negative two, negative one, zero, one, two. I'm going to go up and down forever and ever and ever. But the point is I'm going to be hitting different heights. If I go up and I go down, I'm going to be at different heights. Which doesn't make sense logically with the premise that I want this y equals negative three. I always want a height, I always want a height of negative three. If I keep going up and down on my line, the height is going to change all the time. That doesn't really make a whole lot of sense. That's right here, that's logically, doesn't make sense. That's not going to work. A vertical line here is not going to work. Instead, I'm going to make a horizontal line. Here we go. There's my horizontal line. Now again, let's think about this. Will that line always have a height of negative three? As I go left and as I go right, I don't go up or down or anything like that. My y is always going to stay negative three. Logically that's it. That's what you have to think about when you're thinking about graphing a line of this sort. So this here, y equals negative three is a horizontal line, horizontal line, horizontal line. So I kind of did that in reverse. I actually graphed it first. Negative logically went through the reasoning, whether it made sense to do a horizontal or vertical line. But in this case, it made more sense logically to make a horizontal line. So when you have an equation, y equals negative three, that's a horizontal line and it's a horizontal line that goes through the point negative three on the y axis. All right, so that's the first one. That's logically how I kind of go through these. When I was going through this, when I was going through this in high school, I could not remember even being a math guy as I was. I could not remember the difference between the y's and the x's. So every time I came across a problem like this, I had to just logically think about it. Take my time and think about it. Now you might be a little bit smarter than me. You can just memorize this. That would be a good tactic to use. So all right, let's get to the second one. Now process of elimination, you can probably figure out what the next one is going to be. X equals negative, or excuse me, X equals 1.5. This is going to be a vertical line. That's not being around the bush here. Vertical line, we know that, so let's go ahead and make that point. So 1.5, so again, we want to think I want an x of 1.5. Now I can't say, in this case I can't say a height, so I'm going to say left and right. X's go left and right, so I want a left or right of 1.5. So in this case, that's going to be a right of 1.5. So the line that I create, now remember here's one here, here's two here, so 1.5 is right in the middle. I want to create a line that is always going to go have a right of 1.5. If I create a horizontal line, that doesn't make sense because my lefts and my rights are all over the place. I don't have a constant right of 1.5. So instead of having a horizontal line, I'm going to make a vertical line here and here. This vertical line always has a right of 1.5, always has a right of 1.5. So that's how you can logically go through the difference between a horizontal and a vertical line. But there we go. So actually let me label these real quick. This one is x equals 1.5 and then change my colors down here. This red line is y equals negative 3. Again, that way when you look back in your notes, when you look back at this, you know which one is horizontal, which one is vertical. Okay, that is graphing vertical and horizontal lines. Hopefully this helps and thank you for watching.