Varies directly

Definition

A variable varies directly with another variable if their ratio is constant. Mathematically, $y$ varies directly with $x$ if there exists a constant $k$ such that $y = kx$.

5 Must Know Facts For Your Next Test

1. The equation $y = kx$ represents direct variation, where $k$ is the constant of proportionality.
2. If two variables vary directly, as one increases, the other increases proportionally.
3. The graph of a direct variation equation is a straight line passing through the origin (0,0).
4. To find the constant of proportionality $k$, you can divide $y$ by $x$: $k = \frac{y}{x}$.
5. In problems involving direct variation, solving for one variable typically involves isolating it using algebraic manipulation.

Review Questions

• What is the general form of an equation that shows direct variation?
• If $y$ varies directly with $x$ and $y = 15$ when $x = 5$, what is the value of the constant of proportionality?
• How would you describe the graph of a function where two variables vary directly?

Related terms

Inverse Variation: A relationship between two variables in which their product is constant. If one variable increases, the other decreases proportionally.

Constant of Proportionality: The constant ratio between two directly varying quantities. Represented as 'k' in the equation $y = kx$.

Proportional Relationship: A relationship between two quantities where they maintain a consistent ratio or rate.