This topic summary covers Knowledge Organiser: Real-Life Graphs within Real-Life Graphs for GCSE Mathematics. Revise Real-Life Graphs in Graphs for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 10 of 10 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Knowledge Organiser: Real-Life Graphs
Key Terms
- Distance-time graph: Shows distance from a starting point plotted against time
- Gradient: The rate of change of the y-variable — always read with units
- Conversion graph: A straight line used to convert between two units or currencies
- Fixed charge: The y-intercept of a cost graph; paid regardless of usage
- Rate of change: How quickly one quantity changes relative to another
- Stationary: Not moving — shown as a horizontal section on a distance-time graph
Must-Know Facts
- On a distance-time graph: gradient = speed (include units, e.g. km/h)
- Horizontal line on any real-life graph means the y-quantity is not changing
- Steeper line = faster rate; less steep = slower rate
- Straight line = constant rate; curved line = changing rate
- Negative gradient on a distance-time graph means returning towards the start
- Container filling: wider cross-section → shallower gradient; narrower → steeper gradient
- Always check axis scales and units before calculating gradient
Key Formulas
- Speed = Distance ÷ Time (gradient on a distance-time graph)
- Gradient = (y₂ − y₁) ÷ (x₂ − x₁) — always include units in the answer
- Fixed charge = y-intercept of a cost graph
- Rate per unit = gradient of a cost graph
Common Mistakes
- Units in gradient: Always state the units with the gradient (e.g. m/s, £/km) — a gradient without units loses marks in context questions
- Horizontal sections: A horizontal line on a distance-time graph means the object is stationary (not constant speed)
- Steeper = faster: On a distance-time graph, steeper gradient = greater speed — don't confuse with height on the graph
- y-intercept meaning: The y-intercept is the starting value (e.g. fixed charge, initial distance) — always interpret it in context
Practice questions for Real-Life Graphs
On a distance-time graph, what does a horizontal (flat) section represent?
A distance-time graph shows a section with a negative gradient. Explain what a negative gradient means in the context of a distance-time graph.
Quick recall flashcards
How do you use a conversion graph to convert a value?
1. Find your value on the known axis
2. Draw a line straight up (or across) to the graph
3. Draw a line across (or down) to the other axis
4. Read off the converted value
Always use a ruler for accuracy.
Formula for speed from a distance-time graph?
Speed = gradient = (change in distance) / (change in time)
Speed = (y2 - y1) / (x2 - x1)
Units: always check axes — e.g. km/h, m/s, miles/minute