Like Jean said, the slate (over white) could be carrying the yellow gene because it\'s recessive. Since the others show yellow, I\'d guess it DOES carry yellow.
If you breed the slate to the willow, some of the chicks could be slate. He will pass on the white gene 50% of the time if he has yellow hidden. Even if they are slate/white they will hide yellow. Since the willow shows no white, they are carrying two genes for yellow and will always give a yellow to the young.
Breeding a slate to willow it is a good way to test whether your slate birds are hiding a yellow gene. If they are homozygous for white, NO young will be willow. Of course, ALL of the young will carry yellow and should be removed from the project.