If you have a horizontal line, so let me draw a horizontal line. If you have a horizontal line like that, well then your slope is zero, or you could say your rate of change of y with respect to x is equal to zero. But what about a vertical line? If you have a vertical line like that, what is your rate of change of y with respect to x? Well, some people might say it's infinity, or you could say it's undefined. It's undefined in some way, because at some point, or one way to think about it, you're gonna try to divide by zero because you have a huge change in y over no change in x. Or another way to think about it that's a little bit more in line with that is you could say that your change in x with respect to change in y, notice I took the reciprocal, so now we're talking about a change in the derivative of x with respect to y is equal to zero.