Conversion-Graphs Aqa Higher

Conversion graphs

What is a conversion graph?

• A conversion graph is a straight-line graph relating two quantities

  • You can convert (change) between them by reading values off the graph

• Common examples include

  • Temperature

    • degrees Celsius (°C) and degrees Fahrenheit (°F)

  • Currency

    • Dollars ($) and Yen (¥)

  • Volume

    • Litres and gallons

  • Prices

    • A taxi driver charging per kilometre driven

• The gradient of a conversion graph represents the rate of change

  • If the y-axis is the cost of a taxi journey (£) and the x-axis is the distance travelled (mile) then the gradient represents the cost per mile

    • A gradient of 5 means the cost increases by £5 for each mile travelled

How do I use a conversion graph?

• Find the cost of 20kg using the conversion graph below

  • Start at 20kg on the x-axis

  • Draw a vertical line to the graph

  • Then a horizontal line across to the y-axis

  • Read off the value

    • $12

• Find how many kilograms can be bought with $30

  • Start at $30 on the y-axis

  • Draw a horizontal line to the graph

  • Then a vertical line down to the x-axis

  • Read off the value

    • 50kg

• You can use proportion to find values that on not on the axes

  • To find the cost of 120kg

    • 120kg = 6 × 20kg costs 6 × $12 = $72

    • 120kg = 50kg + 50kg + 20kg costs $30 + $30 + $12 = $72

  • You can only do this if the graph starts at the origin

How do I use a conversion graph that does not start at the origin?

• Convert 100°F into Celsius using the conversion graph below

  • Start at 100°F on the y-axis

  • Draw a horizontal line to the graph

  • Then a vertical line down to the x-axis

  • Read off the value

    • 37.5°C

    • Answers between 37°C and 38°C would be accepted

    • (The true answer is 37.8°C to 1 decimal place)

• The graph starts at 32 on the y-axis

  • This means that 0°C is 32°F

  • This starting value sometimes represents a fixed cost when money is involved

    • It could represent the fixed charge for the cost of a taxi fare

• To convert values that are not on the axis

  • You would need to find an equation for the straight-line