Varies directly

Definition

Two quantities vary directly if they increase or decrease in the same ratio. Mathematically, if $y$ varies directly as $x$, then $y = kx$ for some constant $k$.

5 Must Know Facts For Your Next Test

1. The formula for direct variation is $y = kx$, where $k$ is the constant of proportionality.
2. If the value of one variable doubles, the other variable also doubles in a direct variation relationship.
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 use the ratio $\frac{y}{x} = k$ given any point $(x, y)$ on the line.
5. In polynomial functions, identifying whether variables vary directly can help in modeling relationships between quantities.

Review Questions

• What is the general formula for a direct variation between two variables?
• How does doubling one variable affect the other variable in a direct variation?
• Where does the graph of a direct variation equation intersect the coordinate plane?

Related terms

Constant of Proportionality: A constant value ($k$) that relates two variables in a direct or inverse variation.

Inverse Variation: A relationship where one variable increases as the other decreases, expressed as $xy = k$.

Linear Function: A function whose graph is a straight line and can be written in the form $y = mx + b$.