Linear relationship
A linear relationship has a constant rate of change and can be represented by a straight-line equation. In a two-variable model y = a + bx, b is the change in y for a one-unit increase in x and a is the value at x = 0 when that value is meaningful. A non-zero intercept means the relationship is not direct proportion. A prescribed exact equation differs from a statistical regression line estimated from noisy observations, and either model needs a relevant range and assumptions.
Worked example
A delivery cost model is $100 plus $4 per order. At 20 orders it gives $180; at 30 orders it gives $220. Ten more orders add $40, and the $100 intercept means cost is not directly proportional to orders.
Common mistake
Assuming every straight line passes through zero, or treating a fitted line as proof that changes in one variable cause the other.
Where it appears in your exams
| Qualification | Exam | Relationship | Period |
|---|---|---|---|
| ACCA | PM | Supporting | September 2026–June 2027 |