It is obligatory to keep your back straight while bowing. But is it also obligatory to keep it horizontal?
All you have to do is to bow such that your hands are placed on your knees and stay this way for a while to reach the state you feel rest as in the hadith of the man who prayed badly you may read:
... and then bow, and remain in this state till you feel at rest in bowing ... (See for example here in Sahih al-Bukhari)
As the person who didn't do so has been told that "he didn't pray" we may conclude that this "rest" is necessary and therefore the main obligatory act during ruku' (bowing).
Here some ahadith that describe the act of ruku':
"When the Prophet (ﷺ) bowed he was balanced, he did not make his head higher or lower than his back, and he put his hands on his knees." (Sunan an-Nasa-i and also covered in a longer hadith in Jami' at-Tirmdihi)
... When he bowed, he placed his hands upon his knees and put his fingers below, and kept his elbows (arms) away from his sides, so everything returned properly to its place. ... Thus we witnessed the Messenger of Allah (ﷺ) offering his prayer. (See the full hadith in Sunan abi Dawod and Sunan an-Nasa-i)
... When he bowed he neither kept his head up nor bent it down, but kept it between these extremes ... (Sahih Muslim
I offered prayer beside my father and approximated both my hands and placed them in between the knees. My father told me not to do so and said, "We used to do the same but we were forbidden (by the Prophet) to do it and were ordered to place the hands on the knees." (Sahih al-Bukhari)
So this describes the position of ruku': putting or placing the hands on the knees (not in between), keeping the head in a middle position neither raise it up nor look down too much but try to keep it in the same level as the back, this might lead to a rather horizontal position. So the more you do so the better!
Nevertheless there's a statement that may be used as an evidence of the recommendation to keep the straight while boing in a mursal hadith on the authority of 'Ali ibn abi Talib () saying that the Prophet () used to bow in such a manner that if one had put a full cup of water on his back it wouldn't have dropped (or poured out) this was according to this fatwa compiled by imam Ahmad and abu Dawod in his al-Maraseel (the book on mursal hadith) I couldn't find it so far.
وعن علي رضي الله عنه قال: كان رسول الله صلى الله عليه وسلم إذا ركع، لو وضع قدح من ماء على ظهره لم يهرق، رواه أحمد وأبو داود في مراسيله،