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Quick guide: plain English, key facts and method
In plain English: The gradient of a graph tells you how fast one quantity changes compared with another, such as a speed or a rate of reaction.
Key facts
- Gradient = change in y ÷ change in x.
- The unit of the gradient is (unit of y) ÷ (unit of x), for example cm³/s.
- On a distance–time graph the gradient is the speed.
- A straight line through the origin means the variables are directly proportional.
- Higher: for a curve, draw a tangent at the point and find its gradient to get the rate at that instant.
- Mean rate over a time = total change ÷ total time.
How to do it
- Pick two points far apart on the line (or tangent).
- Find the change in y and the change in x.
- Divide the change in y by the change in x.
- Add the unit.
Memory aid: Rise over run: up ÷ along.