Section 9-9
Joint and Combined Variation
Direct variation describes a simple relationship between two variables. We say y varies directly with x (or as x, in some textbooks) if:
y = kx
for some constant k.
Inverse variation describes another kind of relationship. We say y varies directly with x (or as x, in some textbooks) if:
xy = k,
or, equivalently,
for some constant k.
Joint variation describes a situation where one variable depends on two (or more) other variables, and varies directly as each of them when the others are held constant. We say z varies jointly as x and y if
z = kxy
for some constant k.
Combined variation describes a situation where a variable depends on two (or more) other variables, and varies directly with some of them and inversely with others (when the rest of the variables are held constant). For example, if z varies directly as x and inversely as y, we have the following combined variation equation:
