Definition
Rate of change
Rate of change tells how much one quantity changes when another quantity changes by one unit.
What it means
Watch two quantities move together. First find how much the output changed. Then compare it with how much the input changed. If the input moves 2 steps while the output moves 6, the rate of change is 6 ÷ 2 = 3: three output units for each input unit. A straight-line relationship keeps the same rate; another relationship can have different rates on different stretches.
Remember it
Think “change over change”: how far up for each step across.
Example
A plant is 14 centimetres tall on day 2 and 26 centimetres tall on day 6. Its height changed by 12 centimetres while time changed by 4 days. The rate of change is 12 ÷ 4 = 3 centimetres per day.
Watch for
Do not divide the current output by the current input unless the situation specifically calls for that ratio. Rate of change compares the two changes: output change ÷ input change.
Common mix-up
A rate of change is constant for a linear relationship. It can vary from one interval to another in a non-linear relationship.
Exact meaning
The rate of change between two paired values is the change in the output divided by the corresponding nonzero change in the input. A linear relationship has the same rate of change throughout.