Direct and inverse proportion
Direct and inverse proportion (Extended)
- Direct proportion: $y \propto x$ means $y = kx$ (a fixed multiple).
- Inverse proportion: $y \propto \dfrac{1}{x}$ means $y = \dfrac{k}{x}$ (one rises as the other falls).
- Find the constant $k$ from a known pair, then use it.
- Example: $y \propto x$, $y = 12$ at $x = 3$ → $k = 4$, so $y = 4x$; at $x = 7$, $y = 28$.
Practice
y is directly proportional to x, and y = 12 when x = 3. Find y when x = 7.
k = 12/3 = 4, so y = 4x; at x = 7, y = 28.
Practice
Inverse proportion y ∝ 1/x means:
Inverse proportion: as x rises, y falls, given by y = k/x.
Practice
You find the constant of proportionality k from a known pair of values.
Substitute the known x and y to solve for k, then use the rule.
You've got it
Key idea
- direct: $y = kx$; inverse: $y = \dfrac{k}{x}$
- find $k$ from a known pair, then substitute
- proportion can also be to a square, square root, or cube