Direct & Inverse 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.

This means that as x increases, y increases and as x decreases, y decreases—and that the ratio between them always stays the same.

The graph of the direct variation equation is a straight line through the origin.

Direct Variation Equation
for 3 different values of k

Inverse variation describes another kind of relationship. We say y varies inversely with x (or as x, in some textbooks) if:

xy = k,

or, equivalently,

for some constant k.

This means that as x increases, y decreases and as x decreases, y increases.

The graph of the inverse variation equation is a hyperbola.

Inverse Variation Equation
for 3 different values of k