Grammatically speaking, we would call this a negation.
Do you want to go to the beach today?
No, I do not want to go to the beach today.
Do you like this chocolate cake?
No, I do not like the chocolate cake.
May I borrow your dress for the party tonight?
No, you may not borrow my dress.
In French we form negations by using the following fomula:
Ne + Verb + Pas
Let's use the following example: Je marche avec ma mère. I walk with my mother.
To turn this sentence into a negation you would first find your verb which in this case is "marche," a conjugation of the verb "marcher." You plug the verb into the formula and it turns into "ne marche pas." Put it back in the sentence and you end up with: Je ne marche pas avec ma mère. I don't walk with my mother.
Est-ce que tu manges le gâteau ? (Are you eating the cake?)
Non, je ne mange pas le gâteau. (No, I'm not eating the cake).
Est-ce que tu donnes le livre à ton professeur? (Are you giving the book to your teacher?)
Non, je ne donne pas le livre à mon professeur. (No, I'm not giving the book to my teacher.)
Avec = with
le gâteau (plural: les gâteaux) = cake
le professeur = teacher