Show what is vertical line

Is the line vertical? Determine if the line shown in Fig 1 is vertical and write its equation. The points A and B on the line are at ,3 and , The first coordinate in each pair is the x-coordinate which are , and Since they are equal, the line is vertical. In the interest of clarity in the applet above, the coordinates are rounded off to integers and the lengths rounded to one decimal place. This can cause calculatioons to be slightly off.

Home Contact About Subject Index. Definition: A line on the coordinate plane where all points on the line have the same x- coordinate. 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.

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.