Conversion graphs are straight-line graphs that let you convert (change) between two different units or quantities. Think of them as a translator between two measurement systems.
Common examples:
- Temperature: °C ↔ °F
- Currency: Pounds ↔ Dollars
- Volume: Litres ↔ Gallons
- Prices: Cost vs. quantity (e.g. £ vs. kg)
- Taxi fares: Cost vs. distance travelled
How to Read a Conversion Graph
The process is always the same — draw perpendicular lines to the axes:
To find the y-value for a given x-value:
- Start at your x-value on the horizontal axis
- Draw a vertical line up to the graph line
- From that point, draw a horizontal line across to the y-axis
- Read off the value
To find the x-value for a given y-value:
- Start at your y-value on the vertical axis
- Draw a horizontal line across to the graph line
- From that point, draw a vertical line down to the x-axis
- Read off the value
Tip: Using Proportion
If the graph starts at the origin (0,0), you can use proportion to find values not on the axes. For example, if 20kg costs £12, then 120kg (which is 6 × 20kg) will cost 6 × £12 = £72.
When the Graph Doesn't Start at the Origin
Some conversion graphs have a y-intercept (where they cross the y-axis) that isn't zero. This is important — it often represents a fixed cost.
Example: A taxi company might charge £5 just to turn up (fixed fee), then £2 per mile. If you look at the graph where distance = 0, you'll see the cost is £5, not £0. That's the y-intercept.
Key Rule: You can only use proportion if the graph starts at the origin. If there's a fixed cost (non-zero y-intercept), you must find the equation of the line or read values directly from the graph.
Worked Example: Plumber's Charges
A plumber charges for the time spent on a job. The graph shows price (£) on the y-axis and hours on the x-axis.
Question (a): Estimate the price for a 3-hour job
Solution: At 3 hours, draw a vertical line up to the graph, then a horizontal line to the y-axis. The value reads approximately £225 (answers between £220–£230 are acceptable).
Question (b): A job costs £320. How long did it take (to nearest 0.5 hour)?
4.5 hours
Question (c): What is the fixed callout fee?
y-intercept
£45
Practice Question