Japanese

So, what's the difference between ように and 為に? I've got a sentence in my test here:
看板は遠くからでも見える[ ]大きく書きます

I'm give the choice of using either one or the other. I'm leaning towards the former, but I sure as hell don't know why.

ように　--> in order to
為に --> for the purpose of
Basically the same

also most people donut use the kanji for "tameni", it looks a little pretentious

っ越しました