Direct & Inverse Variation Reference Cheat Sheet

Key Facts

• Direct variation has the form $y = kx$, where $k$ is the constant of variation.
• For direct variation, the ratio $\frac{y}{x} = k$ stays the same for every ordered pair with $x \ne 0$.
• A direct variation graph is a straight line that passes through the origin $(0,0)$.
• Inverse variation has the form $y = \frac{k}{x}$, where $k$ is the constant of variation and $x \ne 0$.
• For inverse variation, the product $xy = k$ stays the same for every ordered pair.
• To find $k$ in direct variation, use $k = \frac{y}{x}$ with any known pair $(x,y)$.
• To find $k$ in inverse variation, use $k = xy$ with any known pair $(x,y)$.
• If $x$ increases in a direct variation, $y$ increases when $k > 0$, but in an inverse variation, $y$ decreases when $k > 0$.

Vocabulary

Direct variation

A relationship where one variable is a constant multiple of another, written as $y = kx$.

Inverse variation

A relationship where the product of two variables is constant, written as $xy = k$ or $y = \frac{k}{x}$.

Constant of variation

The fixed number $k$ that connects the variables in a direct or inverse variation.

Proportional relationship

A relationship with a constant ratio, usually written as $\frac{y}{x} = k$.

Origin

The point $(0,0)$ on the coordinate plane where the $x$-axis and $y$-axis meet.

Ordered pair

A pair of coordinates $(x,y)$ that gives the location of a point or values in a relationship.