How does the symbol of Dr. Eckelburg relate to the theme, the decline of the american dream? Please help :)
By looking at the impact the billboard has on the people in its immediate location rather than the man who put it there, we can relate the eyes of Dr. T.J. Eckelburg to the American dream for the working class. The eyes on the billboard have no substance behind them; they are flat and unseeing, similar to the wealthy businessmen and women, who pass through the Valley of Ashes each day on the train, refusing to see the wasteland between their opulent houses and the fantasy land of Manhattan. Just as Dr. Eckelburg pursues a better location for his practice and abandons the billboard as waste in the already barren wasteland, so do the people aboard the trains abandon and ignore the working class businesses in the Valley of Ashes, leaving them no hope for a future and no hope for the fulfillment of their American dream.
Remember that the giant eyes and glasses were supposed to generate business for Dr. Eckelburg? They were supposed to help him rise up the ladder of American society. However, as the start of Chapter II notes, they are "dimmed," indicating his prospects, and the American dream, have likewise gotten dimmer. What's more, they were supposed to be a sign of prosperity, but they over a "dumping ground." Finally, they are the sign of prosperity, but there is no face to go with them. It is as if the American dream is hollow.
And, as the billboard continues to gather ashes and fall apart, it overlooks Wilson's garage which would serve as the place where Gatsby's (and Daisy's, and Tom's, and Myrtle's, etc. etc. etc.) dream falls apart.