My textbook (A course in modern Japanese, volume two) states the following (Lesson 11 p.26):
In spoken language, sentences are connected with the て-form. And in written language, they are connected with the verb-base and く-form.
The book gives examples for verbs (行って -> 行き) and い-adjectives (高くて -> 高く), but I don't know how to handle な-adjectives. The く-form doesn't appear in the conjugation tables I found in the book. Online, the く-form is mentionned in the case of adverbs, but I am not sure it is the same thing. For example, is the following transformation correct?
このかばんはきれいで, やすい -> このかばんはきれいに, やすい ?
(I found this answer, but it also only mentions い-adjectives)