Thanks for the PR! While we value your contribution, there is concern that the gallery is getting unwieldy. Can you please explain what this example is demonstrating that is not currently being documented in the gallery?

Thanks for this kind message.
I was looking for a way to add axes into my plots.
First I found solutions, which suggested
plt.plot([-10, 10], [0, 0], "k-")
but I think that plt.axvline() is more elegant.
From the existing examples in the api, the use case of plt.axvline() as axes is in my optinion not covered.(https://matplotlib.org/api/_as_gen/matplotlib.axes.Axes.axvline.html?highlight=axvline#matplotlib.axes.Axes.axvline).
Therefore my idea to add this example.

You could add this to the annotating plots example rather than making a new example.

@jklymak : Good point.
I think it's a tradeoff between showing only one idea per example and keeping as few examples as possible.
When I am searching for examples, I prefer to have only one thing that gets explained, ready to copy and paste.
I could also add the axvline to the annotation example , like this:

However I would prefer to make it a new example.

I think grouping similar functionality into fewer examples makes it easier to find things visually rather than having to search a huge page.

IMHO having a dedicated example for axhline/axvline makes sense. (Annotations are quite something different.) For this purpose, I actually like the proposed example. It contains both cases. It‘s a realistic example but still simple enough. However, the title and description should focus on the purpose; something like „Infinite horizontal and vertical lines“ not „Sigmoid function“. The text should explain what the functions create (the infinite h/v Lines at given y/x coordinates) and what this is commonly used for (indicate special values).

Fake8 issues:

./examples/pyplots/sigmoid_function.py:37:1: E402 module level import not at top of file
./examples/pyplots/sigmoid_function.py:42:1: W391 blank line at end of file

The second one is straight forward to solve. To solve the first one, add

    examples/pyplots/sigmoid_function.py : E402

to the per-file-ignores section of .flake8.

That was quite a journey.
@timhoffm Thanks a lot for beeing so patient and guiding me through my first pull request to matplotlib. I think I learned a lot, and hopefully apply this knowledge very soon.

I took the liberty to push a commit renaming the file from sigmoid_function.py to axline.py. - I intend to expand the example with (or at least mention) the recently added axline() function.

Will squash-merge after CI pass.

Thanks a lot, and congratulations on your first contribution to Matplotlib! Hope to see you back some time.