• Direct variation: $y \propto x \Rightarrow y = kx$ (also $\dfrac{y_1}{x_1} = \dfrac{y_2}{x_2}$).
• Inverse variation: $y \propto \dfrac{1}{x} \Rightarrow y = \dfrac{k}{x}$ (also $x_1y_1 = x_2y_2$).
• Joint variation: $y \propto xz \Rightarrow y = kxz$.
• Partial variation: $y = a + kx$ (part constant, part varying).

Steps

1. Write the relationship with the constant $k$.
2. Use given values to find $k$.
3. Write the full equation, then substitute to find the required value.

Changing the subject

Undo the operations in reverse order, doing the same to both sides. Collect the terms containing the new subject together and factorise if it appears more than once.