In Chapter IX of Ethan Frome, why is the affection Ethan and Mattie give each other so apparent?
I am not entirely certain about the intent of your question. How is their affection made so apparent in the chapter, or why is their love emphasized so strongly in this chapter? I will discuss both of these to make sure I have addressed your question.
The love between Mattie and Ethan is very apparent in the beginning of the chapter as Mattie prepares to leave. When Ethan comes home, he is angry that Mattie is upstairs alone trying to bring down her heavy trunk. When he goes upstairs to help her, they have a few moments alone. Mattie has been crying. She thought Ethan was not returning to the farm before she leaves. She had believed she would not be seeing him again. She clings to him as he strokes her hair.
Ethan's strong feelings are also apparent in the scene in the kitchen between Ethan and Zeena. Zeena insists that Jotham Powell will drive Mattie to the train station. When Ethan says he will drive her, Zeena insists even more strongly that Powell will take Mattie and then comes up with some reasons for Ethan to stay on the farm. In this case, Ethan overrules Zeena and leaves with Mattie. He usually gives Zeena her way, but not this time.
In the remainder of the chapter, Ethan and Mattie's deep love for each other is shown in their conversations and actions. For the first time, each one of them speaks freely. The idea of being separated is unbearable for Ethan and for Mattie. They kiss for the first time, and kiss several times after that. When they choose to die together instead of live apart, the depth of their love is emphasized. Because they love each other so desperately, the conclusion of the novel becomes especially tragic.