Graphs in Practical Situations

2026 Syllabus Objectives

By the end of this topic, you should be able to:

  1. Use and interpret graphs in practical situations including travel graphs and conversion graphs
  2. Draw graphs from given data
  3. Interpret the gradient of a straight-line graph as a rate of change
  4. Apply the idea of rate of change to simple kinematics involving distance-time and speed-time graphs, acceleration and deceleration
  5. Calculate distance travelled as area under a speed-time graph
  6. Estimate and interpret the gradient of a tangent at a point (linear sections only)

What Are Practical Graphs?

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Practical graphs are visual tools that show the relationship between two real-world quantities. Instead of just plotting abstract numbers, these graphs help us understand everyday situations like journeys, currency exchanges, or how fast a car is moving.

There are three main types you need to know:

  • Conversion graphs (changing between units or currencies)
  • Distance-time graphs (showing journeys)
  • Speed-time graphs (showing how speed changes over time)

1. Conversion Graphs

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What is a conversion graph?

A conversion graph is a straight-line graph that helps you change between two different quantities. Think of it as a visual calculator that lets you convert one measurement into another.

Common examples include:

  • Temperature: degrees Celsius (°C) to degrees Fahrenheit (°F)
  • Currency: dollars ($) to pounds (£) or yen (¥)
  • Volume: litres to gallons
  • Mass: kilograms to pounds
  • Cost: price per kilogram, taxi fares per kilometre

How to read a conversion graph

To convert from one unit to another:

  1. Find your starting value on one axis (usually the x-axis)
  2. Draw a vertical line upward until it touches the graph line
  3. From that point, draw a horizontal line across to the other axis
  4. Read off the converted value

Example: If a conversion graph shows kilograms on the x-axis and cost in dollars on the y-axis, and you want to find the cost of 20 kg:

  • Start at 20 on the x-axis
  • Draw a line up to the graph
  • Draw a line across to the y-axis
  • Read the value (e.g., $12)

To convert the other way (from cost to kilograms):

  • Start at the value on the y-axis (e.g., $30)
  • Draw a horizontal line across to the graph
  • Draw a vertical line down to the x-axis
  • Read off the value (e.g., 50 kg)

Understanding the gradient

The gradient (slope) of a conversion graph tells you the rate of change — how much one quantity changes for every unit increase in the other.

Example: If a taxi fare graph has:

  • y-axis: Cost in pounds (£)
  • x-axis: Distance in miles

A gradient of 5 means the cost increases by £5 for every mile travelled. This is the cost per mile.

How to calculate gradient:

Gradient=riserun=change in ychange in x\text{Gradient} = \frac{\text{rise}}{\text{run}} = \frac{\text{change in y}}{\text{change in x}}

Graphs starting at the origin vs. graphs with a y-intercept

Starting at the origin (0, 0):

  • When the graph passes through (0, 0), it means zero of one quantity equals zero of the other
  • You can use proportion to find values not on the axes
  • Example: If 20 kg costs 12,then40kgcosts12, then 40 kg costs 24 (double both values)

Starting above the origin:

  • When the graph starts at a value above zero on the y-axis, there is a fixed charge or starting value
  • Example: A taxi fare graph starting at £3 means there's a £3 callout fee before any distance is travelled
  • Example: The Celsius-Fahrenheit graph starts at 32°F because 0°C = 32°F

Important tips

  • Always check the scales on both axes carefully
  • Be precise when reading values from the graph
  • Use a ruler to draw straight lines for accuracy
  • Answers within a reasonable range are usually accepted (e.g., between 37°C and 38°C if the exact answer is 37.5°C)

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