Infinite Gradient: Tangent Parallel to Y/X Axis?

[aurao2003]

Homework Statement

Hi
Can anyone explain the following statement:

When the tangent is parallel to the y-axis it has infinite gradient

Would this be the same condition for a tangent parallel to the x axis? I came across it in the Edexcel C4 textbook.

Cheers

Homework Equations

The Attempt at a Solution

 

[Mentallic]

Since gradient is defined as being rise/run, for a line parallel to the y-axis, if you take a segment of the line that has a rise of, say, 1 and calculate its run, it will be 0. 1/0 is undefined or in a way can be considered infinite. So its gradient is infinite.

Now do the same for a line parallel to the x-axis and see what you get.