1. Solve direct and inverse proportion problems
Solve problems involving direct and inverse proportion, including graphical and algebraic representations
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2. Key vocabulary
Inverse Direct Proportional Equation Constant Value

3. Direct proportion
If two values are in direct proportion when one value doubles then so does the other. Also when one value is zero then so is the other.
When you plot these values on a graph this gives a straight line passing through (0,0).
This table shows the price of apples at a market
Mass of apples (kg) 1 2 5 10
Price of apples (£) 4 20
This is the line graph showing that the mass and price of apples are variables that are in direct proportion (straight line graph through the origin (0,0).
This graph can now be used to find price or mass given the other variable. E.g. £12 = 6kg

4. Direct proportion practice
This table shows the price of plums at a market. Draw a graph to show this and use the graph to find the price of 400g of plums.
Mass of plums (g)
100
200
500
1000
Price of plums (£)
0.5 1
2.5 5

5. Inverse proportion
If two values are in inverse proportion when one value doubles then the other halves. When you plot these values this gives a reciprocal graph.
This table shows the pressure for different forces on an area of 4m2.
Force (N) 1 4 20 40
Pressure (N/m2)
0.25 5 10
The relationship between the values of force and pressure is 4:1 written as a ratio.
Multiplying the pressure by 4 gives the force and so 4P = F or P = 0.25F written as an equation.

6. Inverse proportion practice
Q1: This table shows the relationship between two variables. x 1 2 10 20 y
0.5 5
What is the relationship between the values of x and y written as a ratio.
Write the relationship between x and y as an equation.
The relationship between the values of x and y is 2:1 written as a ratio.
So 2y = x or y = 0.5x written as an equation.
Q2: If it takes 5 builders 20 days to build a wall.
How many days would it take 2 builders to build another wall the same size?
1 builder would take 20 x 5 = 100 days
2 builders would take 100 ÷ 2 = 50 days

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