Variation describes relationship between quantities: (1) Direct variation (x ∝ y means x = ky, increases/decreases together); (2) Inverse variation (x ∝ 1/y means x = k/y, inverse relationship); (3) Joint variation (z ∝ xy means z = kxy); (4) Partial variation (z = a + kx, combination of constant and variable). Formulas: Direct: x₁/y₁ = x₂/y₂; Inverse: x₁y₁ = x₂y₂; Joint: x₁z₁/(y₁) = x₂z₂/(y₂). Solving: (1) Identify variation type; (2) Set up proportion; (3) Find constant k; (4) Apply to new values. Exam tip: Distinguish variation type from problem context. Direct (more input = more output), Inverse (more input = less output).