"You are going to continue eating."

to continue eating = continuar a comer = continuar comendo

"Você continuará comendo" também deveria ser aceitavel

Going to or Will:

When we want to talk about future facts or things we believe to be true about the future, we use 'will'.

-The President will serve for four years. -The boss won't be very happy. -I'm sure you'll like her. -I'm certain he'll do a good job.

If we are not so certain about the future, we use 'will' with expressions such as 'probably', 'possibly', 'I think', 'I hope'.

-I hope you'll visit me in my home one day. -She'll probably be a great success. -I'll possibly come but I may not get back in time. -I think we'll get on well.

If you are making a future prediction based on evidence in the present situation, use 'going to'.

-Not a cloud in the sky. It's going to be another warm day. -Look at the queue. We're not going to get in for hours. -The traffic is terrible. We're going to miss our flight. -Be careful! You're going to spill your coffee.

At the moment of making a decision, use 'will'. Once you have made the decision, talk about it using 'going to'.

-I'll call Jenny to let her know. Sarah, I need Jenny's number. I'm going to call her about the meeting. -I'll come and have a drink with you but I must let Harry know. Harry, I'm going to have a drink with Simon.

Fonte: http://www.englishgrammarsecrets.com/goingtoorwill/menu.php

''you're going to keep eating'' Soaria melhor não acham ?

Essas frases estão ficando cada vez mais passivo agressivas XD

Is continue in the same rule of " Finish,Enjoy, miss and suggest? Every verb after it you put "ing"??