Direct Variation & Proportional Relationships in 2026
A direct variation represents a mathematical relationship between two variables where their quotient remains constant: $y = kx$ or $\frac{y}{x} = k$. Graphically, all direct variations are straight lines that pass precisely through the origin $(0, 0)$.
Physical laws conforming to direct variation include Hooke's Law ($F = kx$), Ohm's Law ($V = IR$), and Newton's Second Law ($F = ma$).
Proportionality Comparison Table
| Relationship Type | Equation | Graph Shape | Behavior as x Increases |
|---|---|---|---|
| Direct Variation | $y = kx$ | Straight line through origin | $y$ increases proportionally |
| Inverse Variation | $y = \frac{k}{x}$ | Rectangular hyperbola | $y$ decreases toward zero |
| Joint Variation | $y = kxz$ | Multi-dimensional plane | Scales with product $xz$ |