If the line has an equation of x = (some number), this is a vertical line. The slope is undefined and all the points on the line have an x-coordinate of that (some number). For example, if x = -2, then all points along this line will have an x-coordinate of -2, making it a vertical line.
In this problem, I’m asked to find the slope of the line x equals -2, and if you guys look at this problem and the answer doesn’t jump out of you right away, that’s okay. This is like a trick question. I mean there’s a real answer, but it’s really a tricky one that a lot of students don’t quite understand until they progress pretty far into their study of slope.
Here is what I’m talking about. Usually when we’re asked to find the equation of a line, I put it into y equals mx plus b form and then the slope is the coefficient in front of x. I don’t have that option in this case because there’s no Ys involved, so that method or that strategy isn’t going to help me.
I personally I’m a visual learner, so it helps me to draw a picture of something like this. If I were to draw the line x equals -2, it’s the vertical line like that, and I can see that this line has a vertical change, but it doesn’t have a horizontal change, so if I had a fraction, I would have some number on top, but on the bottom, I would have zero. In Math, though shall not divide by zero, so we call that undefined or no slope. Either one of those is a valid way of describing the slope of this line. Either one of those is okay.
This is your answer; it’s like a word answer which is also kind of weird in Math, so a lot of students choose to just memorize this fact. If ever you see the equation x equals some constant, it’s always going to be a vertical line like this, and the slope is always going to be either what we call undefined, or a no slope.
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