First Part (Main Answer):
The use of the correct particles (dalelytės) in the given sentences is as follows:
1. Linda has given up work so she can look after her children.
2. Someone gave away the secret plans, and now the boss is angry.
3. The factory gives off a lot of smoke, causing pollution.
4. Although they were losing the match, the team refused to give in.
5. When our supplies give out, we'll have to turn back.
6. The shop is giving away free gifts to anyone who spends more than £30.
Final Answer: The correct particles (dalelytės) have been used appropriately in all of the given sentences.
Second Part (Explanation in Detail):
1. "Given up" is the appropriate phrasal verb in this context, indicating that Linda has quit her job to take care of her children.
2. "Gave away" is used to convey that someone revealed the secret plans, leading to the boss's anger. It implies the act of disclosing something that was meant to be kept secret.
3. "Gives off" is used to describe the emission of smoke from the factory, signifying the source of pollution. It's a phrasal verb commonly used to describe the release of gases or substances.
4. "Give in" means to surrender or admit defeat. In this sentence, the team refused to surrender or give up despite being in a losing position.
5. "Give out" is used to indicate the depletion or exhaustion of supplies. When supplies run out, they are no longer available.
6. "Giving away" implies that the shop is providing free gifts to customers who spend more than £30. It denotes the act of distributing something for free as a promotional offer.
In each of these sentences, the choice of particle (dalelytė) is crucial for conveying the intended meaning accurately.