Directly proportional relationship
Two quantities are directly proportional when one is a constant multiple of the other: y = kx for a fixed constant k. Within that model, the same percentage change in x produces the same percentage change in y, and the line passes through the origin. A linear model with a non-zero intercept is not directly proportional; observed association does not establish a causal relationship or ensure that the rule holds outside the data.
Worked example
If cost is modelled as $4 per unit with no fixed component, 10 units cost $40 and 12 units cost $48. A 20% rise in units produces a 20% rise in modelled cost.
Common mistake
Assuming sales and profit are always proportional, or equating every straight-line relationship with direct proportion despite a non-zero intercept.
Where it appears in your exams
| Qualification | Exam | Relationship | Period |
|---|---|---|---|
| ACCA | PM | Supporting | September 2026–June 2027 |