In what direction did A. Mackenzie cross North America?

Scottish traveler and trader Alexander Mackenzie is the first person to cross the territory of North America (including the part north of Mexico) from the Atlantic Ocean to the Pacific. Arriving in America, he went from New York to the northwest to the shores of Lake Athabasca, and then continued to move along with his companions to the west, and, eventually, reached the Pacific coast. Most of the way he traveled along the river, which is now named after him Mackenzie.