[And so, we are all grateful that the many different directions this took Katara's brain are too fast and numerous for the thought bubble to latch on to any one thought - especially that of herself and Zuko and the love experiment.]

I've got faith in Zuko because I've seen him change. It wasn't easy for him, and I didn't believe him right away, but Zuko proved himself.

...and I'm hoping you will too.

[There. It's not an offer of forgiveness - she never will - and it's not the answer to his question... but it is giving him a way out, if he wants to take it. Yeah, he was a jerk, but the way that he's talking to her it sounds like he's trying and she just - he was dead and now - she just -]