At the beginning of the Parsha, the Torah says, "וימת יוסף וכל אחיו וכל הדור ההוא," indicating that Yosef, all his brothers, and that entire generation died (שמות א:ו'). It was only after this that the period of enslavement of the Jews in Mitzrayim began.
The Ohr Hachaim notes that three "deaths" are mentioned in this Posuk: the death of Yosef, of his brothers, and of the entire generation. He explains that we may learn from this that as long as Yosef was still alive, the Jews in Mitzrayim lived a comfortable and pleasant life. Even after Yosef died, he continues, as long as even one brother was alive, the Egyptians still continued to honor the Jews, presumably as a way of paying tribute to Yosef. Then, even after all the brothers had died, as long as the members of that first generation, the seventy people who first came down to Mitzrayim, were still alive, the Egyptians considered them important people and thus were not able to begin to enslave them. The slavery in Egypt, therefore, did not begin until all three of these deaths had taken place.
Rabbi Chaim Shmuelevitz adds an interesting comment to this idea that as long as the Jews were considered important, the Egyptians couldn't treat them like slaves. One way a person can be considered important by others is to first consider himself important. If a person has a positive attitude about himself, then others will have a positive attitude about him as well. He thus says that as long as the Jews felt important themselves, they would not let themselves be treated as slaves.
This, Rabbi Shmuelevitz says, is the way to combat the Yetzer Hora. The Yetzer Hora influences a person most easily when he feels down or low. A person is most suspectable to temptations when he is depressed and feeling unsatisfied. The Yetzer Hora is thus best able to inspire a person to do Aveiros when the person has a low sense of self-worth. He therefore suggests that one way to avoid being influenced negatively by the Yetzer Hora is to feel good about one's self and improve one's self esteem. (adapted from Growth Through Torah by Rabbi Zelig Pliskin)