C2.9 Graphs in practical situations
- Syllabus
- 0580–2028–2029
- Topic
- C2.9
- Level
- Core
Learning objectives
C2.9.1Interpret practical graphs• Use and interpret graphs in practical situations, including travel and conversion graphs, and interpret the gradient of a straight-line graph as a rate of change.C2.9.2Draw graphs from data• Draw graphs from given data, including distance–time graphs representing journeys.
Interpret travel and conversion graphs in context
A practical graph connects two measured quantities. Read the axis labels, units and scale first; then interpret coordinates and gradients in the situation rather than as isolated numbers.
| Feature on a distance–time graph | Meaning |
|---|---|
| rising segment | distance from the start increases |
| horizontal segment | distance is unchanged, so the traveller is stationary |
| falling segment | the traveller moves back towards the start |
| steeper segment | greater distance change per unit time, so greater speed |
| intersection of two journeys | same distance from the reference point at the same time |
For a straight segment, extgradient=Δextdistance/Δexttime, so its units are a rate such as km/h. A rise of 6 km in 40 minutes is 6/(40/60)=9 km/h.
To read a value, start at the known quantity on one axis, move to the graph, then move parallel to the other axis to read the corresponding quantity. Interpolate between scale marks rather than rounding too early.
A conversion graph maps one unit or currency to another. If the line shows 1 dollar corresponds to 110 yen, $100 corresponds to 11000 yen. To convert in the reverse direction, start from the yen axis and read back to dollars.
When comparing two cost or journey graphs, the lower cost is the lower vertical value at the same horizontal input. At an intersection the values are equal; which graph is cheaper can change after the crossing.
A horizontal distance–time segment means stopped, not travelling at constant speed. A falling segment can still represent positive speed towards the start; the sign records direction of distance change, while speed is the magnitude of the gradient.
Draw practical graphs from data and journey stages
A practical graph is built from ordered data pairs. Choose labelled axes and a scale that uses the grid well, plot each pair accurately, and join points in the way the context supports.
| Step | Drawing decision |
|---|---|
| 1 | put the independent quantity, usually time, on the horizontal axis |
| 2 | label both axes with quantities and units |
| 3 | choose simple uniform scales covering all values |
| 4 | calculate any missing endpoint values or times |
| 5 | plot coordinates accurately and join required straight journey segments |
| 6 | check every endpoint against the narrative |
Starting at 15:00 and distance 0, walking for 20 minutes at 4.5 km/h covers 4.5imes20/60=1.5 km, so draw from (15:00,0) to (15:20,1.5). Running a further 6 km in 40 minutes ends at (16:00,7.5).
A stop is a horizontal segment from the arrival time to the departure time. A return to the starting point is a segment ending at distance 0; calculate its endpoint time from exttime=extdistance/extspeed.
For a proportional conversion, include the origin. If 1 litre is 0.22 gallons, useful pairs include (0,0) and (100,22); plot them and draw one straight line through both.
When data are supplied in a table, keep coordinate order consistent and use the graph type requested. Do not force a line through the origin unless the context states zero of one quantity corresponds to zero of the other.
On a distance–time graph, plot cumulative distance, not speed. Constant speed appears as a straight sloping segment; a faster stage is represented by a steeper gradient rather than a larger labelled speed value on the vertical axis.