Horizontal and Vertical Lines

[One speaker] 

[Presentation starts with the problem on the screen:

What is the equation of the horizontal line through (-4,6)?
________]

Instructor: What is the equation of the horizontal line through the point (-4, 6)? 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. [Draws a vertical line.] So (-4, 6), that’s gonna be in the second quadrant. [Draws a horizontal line through the vertical line making a graph.] So this is my x-axis, that is my y-axis. [Labels the horizontal line as the x-axis, and the vertical line as the y-axis.] I’m gonna go -4 in the x-direction. So 1, 2, 3, 4, -4. [Marks on the x-axis four marks left of the x-axis.] 1, 2, 3, 4, 5, then 6 in the y-direction. [Marks on the y-axis 6 marks up from the x-axis.] So the point that we care about is going to be right over there, (-4, 6). [Puts a point that is 4 marks to left of the y-axis but also 6 points above the x-axis.] And what is the equation of the horizontal line? It is a horizontal line [underlines “horizontal line” from the question]. So it’s just gonna go straight left-right like this. [Draws a line parallel with the x axis running through the point at (-4, 6).] 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 6. [Writes “y=6”] This is the equation, y is equal to 6. Doesn’t matter what x you input here, you’re gonna get y=6. It just stays constant right over there. So the equation is y equals 6. [Writes y=6 in the answer box for the question.] Let’s do another one of these.

[The following multiple choice is presented:
What is the slope of the line y=-4?

• -4
• 0
• 4
• Undefined]

So here we are asked, “What is the slope of the line y=-4?” 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. [Draws another graph.] X-axis, y-axis. [Labels the axis of the graph.] And the slope of the line, y = -4. So for whatever x you have, y is gonna be -4. [Puts a mark beneath the x-axis on the y-axis and labels it -4.] Let’s say that’s a -4 right over there. And so, the line is y equals -4. So I can draw it like this. [Draws a horizontal line running through -4 on the y-axis.] 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. [Writeson the screen.] 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 [there is a horizontal line going through -4 on the y-axis]. Y doesn’t change, no matter how much you change x. [Marks 0 of the options available to answer the question.] Let’s do another one of these. This is fun.

[Next problem is shown:
What is the slope of the line x=-3?

• -3
• 0
• 3
• Undefined]

So now they are asking us, “what is the slope of the line x equals -3”? Let me graph that one. So, I’m just going to draw my axis real fast [draws graph with the x and y-axis]. X-axis. Y-axis. X is equal to -3. So -1, -2, -3 [makes marks to indicate the previous numbers going across the left side of the x-axis]. 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 -3. So, it would look like this [draws a vertical line through -3]. X is equal to -3. 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 for change in x. Change in y for change in x. [Writeson the screen.] 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 [selects the “undefined option from the question presented]. Let’s do one more.

[Next problem is “What is the equation of the vertical line through (-5,-2)?”]

What is the equation of the vertical line through (-5, -2)? So, let me do this one 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 [writes “x doesn’t change” with “x=” below it]. Well, if it contains the points (-5, -2), so if it has a point where X is equal to -5 and if X never changes, it’s a vertical line. Well, that means its equation has to be X is equal to -5. And we can draw that out if it helps. So let me draw that out [draws a graph with an x and y-axis]. So, I need to make sure that’s a straight line. Okay, so we have X, and we have Y [labels the axis]. So we have the point (-5,-2). So -1, 2, 3, 4, 5 [makes these marks on the negative side of the x-axis]. -1,-2 [makes these marks on the y-axis]. 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 [draws a vertical line through -5 on the axis]. And so notice, X never changes. No matter what Y is, X is equal to -5. This has an undefined slope. It is a vertical line. Its equation is X is equal to -5.

[End of video.]