Reading the Graph: To convert a value from the x-axis, move vertically up to the line, then horizontally across to the y-axis to find the corresponding value.
Inverse Conversion: To convert from the y-axis back to the x-axis, move horizontally to the line and then vertically down to the x-axis.
Scaling (Extrapolation): If a value is beyond the range of the axes, you can use a smaller known conversion and multiply it. For example, if units convert to , then units must convert to (provided the graph starts at the origin).
Direct Proportion Graphs: These start at . They are used for simple conversions like currency or weight where zero of one unit equals zero of the other.
Fixed-Base Graphs: These do not start at the origin (e.g., Temperature or Taxi Fares). The y-intercept represents a fixed starting value or offset that must be accounted for in every conversion.
| Feature | Direct Proportion | Fixed-Base |
|---|---|---|
| Intercept | where | |
| Scaling | Simple multiplication works | Requires equation |
| Example | Currency Exchange | Celsius to Fahrenheit |
Check the Scales: Always identify the value of each small grid square on both axes before reading points, as the x and y scales are rarely the same.
Use a Ruler: When drawing lines from the axes to the graph, use a ruler to ensure accuracy; even a small deviation can lead to an incorrect reading.
Sanity Check: Verify if your answer makes sense. If the graph shows that unit of A is roughly units of B, your final answer should reflect that approximate ratio.
Multiple Steps: For values far outside the graph's range, find a convenient point (like or ), convert it, and then scale the result.
Misapplying Scaling: Students often try to multiply values for graphs that do not start at the origin. This is mathematically incorrect because the fixed intercept () does not scale linearly with the gradient.
Axis Swapping: Ensure you are starting on the correct axis. Converting 'A to B' requires starting on the axis labeled 'A'.
Rounding Errors: Reading between grid lines requires estimation. If a point falls between and , do not simply round to the nearest whole number unless the question specifies it.
