Conversion Graphs (IGCSE Maths)
A conversion graph is a straight-line graph used to switch between two units or quantities in one quick step. On this page you will learn how to draw a conversion graph from a given rate, how to read off values in both directions using the dotted-line technique, and how to handle graphs that do not pass through the origin (such as phone tariffs or hire charges with a fixed fee). Fully worked examples show every step, and the auto-marked practice rooms below let you build speed and confidence at your own pace.
What is a conversion graph?
A conversion graph is a straight-line graph that lets you quickly convert between two units or quantities. Instead of calculating each time, you simply read a value off one axis and trace across to the other.
Typical exam uses include converting between currencies, units of length or mass, temperatures, speeds, and fuel volumes. The key principle is that a fixed rate produces a straight-line relationship, so two points are enough to draw the full graph.
Through the origin?
If zero in one unit equals zero in the other (e.g. km and miles), the line passes through \((0, 0)\). Both axes start at the same point.
Not through the origin?
Some real-life graphs have a fixed starting value (e.g. a taxi fare with a fixed pickup charge). The line intercepts the vertical axis above zero.
Readings are approximate
Because you are reading off a graph by eye, answers are not exact. Exam mark schemes allow a tolerance range around the correct value.
US$ to Rand Conversion ($1 = R20)
US$ (dollars)
Read up from $30 on the x-axis, then across to the y-axis to get R600
Taxi Fare: R30 fixed + R10 per km
Distance (km)
Read up from 20 km, then across to the y-axis to get R230. The line does not start at the origin.
How to draw a conversion graph
You only need two points to draw a straight line. The simplest approach is to pick the two extremes of your range.
Label both axes clearly, include units, and add a title to the graph.
How to read off a conversion graph
Use the dotted-line technique shown in the diagrams above:
To convert in the reverse direction (B to A): start on the y-axis, rule horizontally to the graph line, then rule vertically down to the x-axis.
Worked Examples
💡 Example 1: Currency, through the origin
On a certain day, $1 = 20 rand (R). Draw a conversion graph for $0 to $50, then use it to convert:
(i) $30 to rand (ii) R600 to dollars
Step 1: find two key points.
When $0 is converted: R0 (the line starts at the origin)
When $50 is converted: 50 × 20 = R1000
Step 2: plot (0, 0) and (50, 1000), join with a straight line.
Step 3: use the dotted-line technique to read off.
(i) $30 → R600
(ii) R600 → $30
Graph readings are approximate; here the values land on the gridlines so they read exactly, but in general expect a small rounding difference.
💡 Example 2: Not through the origin (taxi fare)
A taxi charges a fixed pickup fee of 30 rand plus 10 rand per kilometre. Draw a conversion graph for 0 to 25 km, then find the fare for a 20 km trip.
Step 1: write the equation.
\[ C = 10d + 30 \qquad (0 \le d \le 25) \]Step 2: find two points.
\[ \begin{aligned} d &= 0: \quad C = 30 \\ d &= 25: \quad C = 10 \times 25 + 30 = 280 \end{aligned} \]Step 3: plot \((0, 30)\) and \((25, 280)\), join with a line.
Step 4: use the dotted-line technique to read off at \(d = 20\).
\[ C \approx 230 \text{ rand} \]Exact check: \(10 \times 20 + 30 = 230\). ✓
⚠️ Common mistakes to avoid
- Assuming the line goes through the origin when there is a fixed starting value. Always check.
- Swapping the axes when reading off. Trace horizontally from one axis, then vertically to the other.
- Using a value outside the drawn range. A conversion graph is only reliable within the range it is drawn for.
- Forgetting units in your answer.
📌 Key Points
- A conversion graph is a straight line because the rate of conversion is constant.
- Graphs that convert proportional quantities (e.g. km to miles) pass through the origin.
- Graphs with a fixed starting charge do not pass through the origin; the line crosses the vertical axis above zero.
- Readings from a graph are approximate, not exact.
- Two points are enough to draw the line; choose the endpoints of the required range.
Ready to practise? The questions below start gentle and build up to multi-step problems.