



Y can
vary directly as X, but Y can also vary inversely as X.



That
means that when X goes up, Y goes down. 


The
inverse of X is ^{1}/X. 


We might
also need the unit conversion constant k. 


That
makes the basic inverse variation equation form: 











Another
type of variation is joint variation. 


That
means that Y varies "jointly" as more than one thing. 


The trick
is, that these things are MULTIPLIED not added. 


So
"Y varies jointly as X and Z" means: 





Y = kXY






Don't
forget the unit conversion constant "k" 





We can
put a bunch of these together. 


We could
say: 


"Y
varies directly as X and inversely as Z" 


That
translates to: 








The trick
to these is that even though the words say things like X AND
Z, 


all the
stuff on the right side gets multiplied together. 





So far,
we have just used single letters for what Y varies to, 


but we
could use all kinds of stuff. 





We could
say "Y varies inversely to X ^{2}" 


That one
is: 








You'll
probably see one with all kinds of stuff thrown in, 


kind of
like a fireworks grand finale: 


"Y
varies directly as X ^{3} and the square root of Z 


and
inversely as W ^{5} and log T" 


Would
look like this: 








copyright 2005 Bruce Kirkpatrick 
