Graphs
Interpreting graphs
A real-life graph tells a story. The steepness is the rate — how fast something is changing — and a flat line means nothing is changing at all.
Reading the axes first
Before anything else, look at what each axis shows and what units it uses. A graph of distance against time is a completely different thing from a graph of speed against time, even if the lines look identical. The axis labels tell you what the story is about.
What the steepness means
The STEEPNESS of a line shows the RATE OF CHANGE. A steep line → the quantity is changing quickly. A gentle slope → it is changing slowly. A FLAT line → it is not changing at all. On a distance–time graph, a flat line means stopped — not 'going slowly'.
Up, down and level
Read from left to right and describe each part in turn. Rising → increasing. Falling → decreasing. Level → staying the same. 'The water heated quickly for 10 minutes, then stayed at the same temperature, then cooled slowly.' That is a full description of three sections.
Reading values between points
Because the line is continuous, you can read off values you were never given. Go up from the x-axis to the line, then across to the y-axis. This is an estimate rather than a measurement — but a sensible one, and it is the main reason graphs are drawn as lines rather than dots.
Worked examples
What does a flat line mean?
- The value on the y-axis is not changing.
- Time is still passing along the x-axis.
Answer: The quantity is staying the same
Comparing two slopes
- One line is steeper than the other.
- Steepness shows the rate of change.
Answer: The steeper line is changing faster
A flat section on a distance–time graph
- Distance is not increasing.
- But time is still passing.
Answer: The object has stopped
Reading between two points
- At 10 minutes it was 3 °C; at 20 minutes it was 5 °C.
- 15 minutes is halfway between them.
- So the value is about halfway too.
Answer: About 4 °C
Describing a graph in words
- It rises steeply, then levels off, then falls.
- Match each shape to what it means.
Answer: It increased quickly, stayed the same, then decreased
Where you see this in real life
- A hospital chart of a patient's temperature shows at a glance whether it is rising or settling.
- A graph of a journey shows where the car stopped — the flat sections.
Key words
- Rate of change
- how quickly one quantity changes compared with another
- Steepness
- how sharply a line rises or falls
- Axis
- one of the two number lines on a graph
- Continuous
- changing smoothly, with no gaps
- Interpret
- explain what something means