This PoSWW (as is the accompanying WitCH) is from Cambridge’s *Mathematical Methods Units 1 and 2*. and is courtesy of the Evil Mathologer. (A reminder, we continue to post on Cambridge not because their texts are worse than others, but simply because their badness is what we get to see. We welcome all emails with any suggestions for PoSWWs or WitCHes.)

We will update this PoSWW, below, after people have had a chance to comment.

## Update

Similar to Witch 6, the above proof is self-indulgent crap, and obviously so. It is obviously not intended to be read by anyone.

One can argue how much detail should be given in such a proof, particularly in a subject and for a curriculum that systemically trashes the concept of proof. But it is difficult to see why the diagram below, coupled with the obvious equations and an easy word, wouldn’t suffice.

So, why do lines need to go through (0,0) to enable the gradients to be calculated and/or triangles to be formed with the x-axis?

Again, not saying this is the only problem – but it seems a bit irrelevant.

I found this proof, http://mathforum.org/library/drmath/view/54476.html, it’s so much more concise. Removes the need for the origin, as you are looking a the rise / run of two lines. So yeah, just over complication.

Thanks, mrpotaczala. Of course there is absolutely no need for the tediousness of the above proof. The typesetting isn’t great, but the mathforum link you included is more than enough. See the update above.

Yes Number 8, and probably worse than irrelevant. The whole notion of gradient is that it refers only to change, and so the specific position/values are best ignored if possible.