Definition
Linear relationship
A linear relationship connects two quantities with a constant rate of change, so its graph lies on a straight line.
What it means
Watch how one quantity changes when the other takes equal steps. If the change repeats by the same amount each time, the relationship is linear. A starting amount may shift the line away from zero without changing the constant rate.
Remember it
Same step across, same change up or down.
Example
A taxi charges $4 before the journey and $2 per kilometre. The relationship is y = 2x + 4. At 0, 1, 2, and 3 kilometres, the fares are $4, $6, $8, and $10, increasing by $2 each step.
Watch for
This taxi relationship is linear but not proportional, because it starts at $4 instead of passing through (0, 0).
Common mix-up
Linear describes a constant rate, not simply a pattern that increases. An increasing curve can still be nonlinear.
Exact meaning
A linear relationship between two numerical quantities has a constant rate of change: equal changes in the input produce equal signed changes in the output. It can be represented in a form such as y = mx + b, and its plotted points lie on a straight line.