Rate of Change – Gradient in the Real World
The rate of change is simply the real-world name for a gradient: it tells you how quickly one quantity changes compared to another, such as litres per minute, kilometres per hour, or dollars per item. Every linear relationship's gradient can be read as a rate of change – the abstract number m in y = mx + c becomes something concrete and meaningful once it's attached to real units.
Once you know a rate of change and a starting value, you can predict future values without needing a graph or table at all – simply add the rate, multiplied by however many extra steps you need, to the starting value.
Calculating and Using a Rate of Change
Rate of change = (change in quantity) ÷ (change in time or steps). To predict a future value: future value = starting value + (rate × number of steps).
(100 − 40) ÷ 5 = 60 ÷ 5 = 12 litres/min.
30 + (4 × 6) = 30 + 24 = 54 cm.
Real-Life Application
- Speed: the rate of change of distance over time.
- Fuel efficiency: the rate of change of fuel remaining over distance travelled.
- Population growth: the rate of change of population over years.
Key Takeaways
- Rate of change is the real-world meaning of a gradient.
- It is calculated as (change in output) ÷ (change in input).
- Future values can be predicted using: starting value + (rate × steps).
Practice: Rate of Change
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