Can stuff such as "CFLAGS=-g" be passed to sub-makes?

[Arthur David Olson]

If I'm doing recursive makes, with a "makefile" rule such as
	whatever whateverelse:
		-cd subdir1 ; $(MAKE) -$(MAKEFLAGS) $@
		-cd subdir2 ; $(MAKE) -$(MAKEFLAGS) $@
is there some way I can arrange things so that if I use the command
	make whatever CFLAGS=-g
the "CFLAGS=-g" will be passed to the sub-makes?

Please mail me any replies, rather than posting an article.  Thanks.
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