〜ように (as)
as, just as
Verb plain form + ように · Noun + のように · 次のように
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ように also means "as", pointing to something already said, known or shown: 前にも言ったように、明日は休みです, "as I said before, tomorrow's a day off".
Common set phrases: ご存じのように, "as you know"; 次のように, "as follows"; 図のように, "as shown in the diagram"; 予想したように, "as expected".
This ように comes at the start of a sentence and sets up what follows. That's different from the N4 ように, "so that", which gives a goal: 忘れないようにメモする.
Before a verb, it's ように; before a noun, it's ような: 次のような問題, "problems like the following". In casual speech, みたいに does the same job after verbs and nouns, without の.
Examples
前にも言ったように、明日は休みです。
As I said before, tomorrow is a day off.
ご存じのように、来月から料金が変わります。
As you know, prices change from next month.
図のように、線を引いてください。
Please draw a line as shown in the diagram.
次のように書いてください。
Please write it as follows.
天気予報で言っていたように、雨が降ってきた。
Just as the forecast said, it's started to rain.