Horizontal & vertical lines

- [Instructor] What is the equation of the horizontal line through the point negative four comma six? So let's just visualize this. Once you get the hang of it, you might not have to draw a graph, but for explanatory purposes, it might be useful. So negative four comma six, that's going to be in the second quadrant. So if this is my x-axis, That is my y-axis. I'm going to go negative four in the x direction. So one, two, three, four. Negative four. And then one, two, three, four, five, six, in the y direction. So the point that we care about is going to be right over there. Negative four comma six. And what is the equation of the horizontal line? It is a horizontal line. So it's just going to go straight left, right like this. That is what the line would actually look like. So what is that equation? Well, for any x, y is going to be equal to six. This is the equation, y is equal to six. Doesn't matter what x you input here, you're gonna get y equals six. It just stays constant right over there. So the equation is y is equal to six. Let's do another one of these. So here we are asked what is the slope of the line y is equal to negative four? So let's visualize it and then in the future, you might not have to draw it like this. But let's just draw our axis again. X-axis y-axis and the slope of line y equals negative four. So for whatever x you have, y is going to be negative four. Let's say that's negative four right over there. And so, the line is y the line is y equals negative four. So I can draw it like this. So what's the slope of that? Well, slope is change in y for given change in x. And here, no matter what I change my x, y doesn't change. It stays at negative four. My change in y over change in x. Doesn't matter what my change in x is. My change in y is always going to be zero. It's constant. So the slope here is going to be equal to zero. Y doesn't change, no matter how much you change x. Let's do another one of these. This is fun. So now they are asking us, what is the slope of the line x equals negative three? Let me graph that one. So, I'm just going to draw my axis real fast. X-axis y-axis X is equal to negative three. So negative one, negative two, negative three. And so, this line is going to look let me, it's going to look like this. No matter what y or you can say no matter what y is. X is going to be equal to negative three. So, it would look like this. X is equal to negative three. So what's the slope here? Well, it's undefined. A vertical line has an undefined slope. Remember, you want to do what's your change in y or change in x. Change in y or change in x. Well, you can think about what's the slope as you approach this but once again, that could be, some people would say, maybe it's infinite, maybe it's negative infinity. But that's why it's undefined. A vertical line is going to have an undefined slope. So we'll go with undefined. Let's do one more. What is the equation of the vertical line through negative five comma negative two? So, let me do this without even drawing it. I'll draw it right after that. So, if we're talking about a vertical. If we're talking about a vertical line, that means that x doesn't change. X doesn't change. If we were talking about a horizontal line, then we'd say y doesn't change. So if x doesn't change, that means that x is just going to be equal to some constant value. Well, if it contains the points negative five comma negative two, so if it has a point where x is equal to negative five and if x never changes, it's a vertical line, well that means its equation has to be x is equal to negative five. And we can draw that out, if it helps. So let me draw that out. So, I need to make sure that's a straight line. Okay, so we have x, and we have y, so we have the point negative five comma negative two. So negative one, two, three, four, five, negative one, two so we want to go have a vertical line that goes through that point. So a vertical line, well that just goes straight up and down. So it's just going to look like this. And so notice, x never changes. No matter what y is, x is equal to negative five. This has an undefined slope. It is a vertical line. Its equation is x is equal to negative five.