老师问我Do you like sports?

当然是的。。。

do you... --> yes i do / no i don't
are you... --> yes i am / no i'm not
can you... --> yes i can / no i can't

以此类推。

A good question.

"like" as a transitive verb have the meaning you wants to indicate. But you also shoul know that there must be a noun after the transitive verb, so it is right when you answer is "Yes, I like sports"or"Yes I like it". Noun should not be omited after the V.T.

But when you open your dictionary, you will find "like" can be a V.i(intransetive verb) in many cases. So it is nacessary for me to point it out that in this usage, "like" often means "preferance" or "inclination". For instance, "If you like, we can go there."

do 是用来强调后面的动词
经常看电影就知道了
比如说 i do hear what you said
还有很多例子一时想不起来><

或者，还有你可以不用说 yes
而是 question： do you like sports
answer