Direct variation

Definition

Direct variation describes a linear relationship between two variables where one variable is a constant multiple of the other. Mathematically, it is expressed as $y = kx$, 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 $k$ represents the slope of the line in a direct variation equation.
4. If $y$ varies directly with $x$, then $\frac{y}{x} = k$ for all pairs $(x, y)$.
5. In problems involving direct variation, solving for $k$ can help find unknown values given one pair of variables.

Review Questions

• What is the general form of a direct variation equation?
• How does changing the value of $k$ affect the graph of a direct variation?
• If $y$ varies directly with $x$, and you know that when $x = 3$, $y = 9$, what is the constant of variation?

Related terms

Inverse Variation: A relationship between two variables in which their product is constant. Mathematically expressed as $xy = k$ or $y = \frac{k}{x}$.

Constant of Variation: $k$ in direct and inverse variation equations representing how much one variable changes relative to another.

Linear Function: A function that creates a straight line when graphed. It has the form $f(x) = mx + b$, where $m$ and $b$ are constants.