In Act I of Arthur Miller's Death of Salesman, what is the significance of Willy's exchange with The Woman?

In Arthur Miller's play, Death of a
Salesman, the exchange with the Woman is significant because it shows that
Willy has had an affair with a secretary in Boston. This scene does not indicate if the
affair is still going on, but the audience learns that Willy brings her gifts and she
find him funny. His ego is further bolstered by her pronouncement that
she chose him of all the other salesman in and
out of her office. Willy definitely appreciates the feeling, as he has just finished
telling his wife how lonely it gets on the road when business isn't
good.

It is significant that whereas Linda is truly
dedicated to her husband, and in her eyes he is a successful father, husband and
salesman, Willy lies to Linda by committing adultery, and lies also when he says he is
lonely. It seems he then must also be lying when he
says,

On the
road—on the road I want to grab you sometimes and just kiss the life outa
you.

This may be how he is
feeling when he says it at home, but on the road, he obviously would not be concerned
about Linda when he's busy with someone else. This also shows us that the relationship
between Willy and Linda has not always been good. It would also appear that the Woman
represents another example of appearance vs reality. While all appears well between
Linda and Willy, as Linda's voice overlaps with the Woman's voice, we find that Willy
has not been faithful. And while Linda and Happy may not know of Willy's indiscretion,
we will learn that Biff does, which simply complicates the family
dynamics as the play progresses.