A vertical line is all rise. If there is no y value then how does this become a line in the x-y plane?
It is not that there is NO y value, but that there are an INFINITE number of y values.
A vertical line is represented by an equation in the form of x = constant, where "constant" can be any real number. It is true that a vertical line does not have a specific y value associated with it because the y coordinate can take on any value. However, this does not mean that it does not exist in the x-y plane.
To understand how a vertical line becomes a line in the x-y plane, let's consider its graphical representation. In the x-y plane, the x-axis represents the horizontal direction and the y-axis represents the vertical direction. A vertical line is a line that extends infinitely in the y-direction (up and down) but does not change in the x-direction (left and right).
So, when we plot a vertical line on the x-y plane, we draw a straight line that goes up and down and passes through all possible y-values, while the x-value remains constant. The line's slope is undefined because there is no change in the x-coordinate, resulting in a vertical line that extends infinitely in both the positive and negative y-directions.
In summary, even though a vertical line does not have an associated y value, it is still a valid line in the x-y plane because it vertically extends infinitely while maintaining a constant x-coordinate.