1. **State the problem:** We need to find the relationship between the mass of sugar (in kg) and its cost (in pence) given that sugar costs 80p for every 2 kg.
2. **Identify the formula:** The cost is proportional to the mass. We can write the cost $C$ as a function of mass $m$:
$$C = k \times m$$
where $k$ is the cost per kg.
3. **Calculate the cost per kg:** Since 2 kg costs 80p,
$$k = \frac{80}{2} = 40$$
So, the cost per kg is 40p.
4. **Write the function:**
$$C = 40m$$
This means for every 1 kg increase in mass, the cost increases by 40p.
5. **Create a table of values:**
| Mass (kg) | Cost (p) |
|-----------|----------|
| 0 | 0 |
| 1 | 40 |
| 2 | 80 |
| 3 | 120 |
| 4 | 160 |
| 5 | 200 |
| 6 | 240 |
| 7 | 280 |
| 8 | 320 |
| 9 | 360 |
| 10 | 400 |
6. **Plotting the line:** On the graph, plot points from the table and draw a straight line through them. The line starts at (0,0) and goes up with slope 40.
This line shows the linear relationship between mass and cost.
Sugar Cost
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