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*