# Write a vertical line in slope intercept form

Just as a "Z" with its two horizontal lines is not the same as an "N" with its two vertical linesso also "Zero" slope for a horizontal line is not the same as "No" slope for a vertical line.

## Horizontal line in point slope form

Don't mix them up! And just to make sure that this gels with all of these other formulas that you might know-- but I want to make it very clear. If I rise a ton when I run a little bit, if I move a little bit in the x direction, and I rise a bunch, then I have a very steep line. And then we would call this x2 and we would call this y2, if this is our start point and that is our end point. These are all different variations in slope, but hopefully you'll appreciate that these are measuring inclination. This relationship is always true: a vertical line will have no slope, and "the slope is undefined" or "the line has no slope" means that the line is vertical. And so the slope here, the change in y, y2 minus y1. So if we start over here, our change in x is going to be negative So the line that connects these two points will look like this. Let me just do a quick graph of these just so we can visualize what they look like. So maybe the slope will be negative? If I go from negative 3, negative 1 to 7, negative 1, I'm running a good bit.

In both cases, the number multiplied on the variable x was also the value of the slope for that line. My y value does not change no matter how much I change my x value. The graph looked like this: Notice how the line, as we move from left to right along the x-axis, is edging downward toward the bottom of the drawing; technically, the line is a "decreasing" line.

It will look like that.

What number is neither positive nor negative? So the slope of this and any other horizontal line should, logically, be zero.

## Slope of a vertical line

From the line's graph, I'll use the arbitrary points 4, 5 and 4, —3. And that's actually what's happening here. This, of course, is the y-axis. Now, they're asking us to find the slope of the line that goes through the ordered pairs. And just to make sure that this gels with all of these other formulas that you might know-- but I want to make it very clear. The graph looked like this: Notice how the line, as we move from left to right along the x-axis, is edging downward toward the bottom of the drawing; technically, the line is a "decreasing" line. And so the slope here, the change in y, y2 minus y1.

But our change in y is still going to be 0. So the slope here is 0.

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