Direct variation

Definition

Direct variation describes a linear relationship between two variables where one variable is a constant multiple of the other. It is represented by the equation $y = kx$, where $k$ is the constant of variation.

5 Must Know Facts For Your Next Test

1. In direct variation, as one variable increases, the other variable increases proportionally.
2. The graph of a direct variation equation is a straight line passing through the origin (0,0).
3. The constant of variation $k$ in the equation $y = kx$ can be found by dividing $y$ by $x$ ($k = \frac{y}{x}$).
4. If $k > 0$, both variables increase together; if $k < 0$, one variable decreases as the other increases.
5. Direct variation is different from inverse variation, where the product of the two variables remains constant.

Review Questions

• What does the graph of a direct variation look like?
• How do you find the constant of variation in a direct variation equation?
• What happens to one variable if it directly varies with another and that second variable doubles?

Related terms

Inverse Variation: A relationship between two variables where their product is constant. Represented by the equation $xy = k$.

Constant of Variation: The constant factor in a direct or inverse variation equation. In direct variation, it is denoted by $k$ in $y = kx$.

Linear Function: A function that creates a straight line when graphed. Represented generally as $y = mx + b$, where both $m$ and $b$ are constants.