1. The problem involves understanding the relationship between cost and mass of sweets for two packaging types: Box and Bag. 2. The graph shows cost (pence) on the vertical axis and mass (grams) on the horizontal axis. 3. For the Box, the cost increases gradually with mass, indicating a lower rate of cost increase per gram. 4. For the Bag, the cost starts lower but increases more steeply, indicating a higher rate of cost increase per gram. 5. To find the cost function for each, we use the formula for a linear relationship: $$\text{Cost} = m \times \text{Mass} + b$$ where $m$ is the slope (rate of cost increase per gram) and $b$ is the y-intercept (initial cost). 6. From the graph, estimate points for Box: (0,0) and (400, 150). Slope for Box: $$m = \frac{150 - 0}{400 - 0} = \frac{150}{400} = 0.375$$ 7. Cost function for Box: $$\text{Cost}_{Box} = 0.375 \times \text{Mass}$$ 8. For Bag, estimate points: (0, 50) and (400, 200). Slope for Bag: $$m = \frac{200 - 50}{400 - 0} = \frac{150}{400} = 0.375$$ 9. Cost function for Bag: $$\text{Cost}_{Bag} = 0.375 \times \text{Mass} + 50$$ 10. Interpretation: The Box has no initial cost and increases cost steadily, while the Bag has an initial cost of 50 pence plus the same rate of increase per gram. Final cost functions: $$\text{Cost}_{Box} = 0.375 \times \text{Mass}$$ $$\text{Cost}_{Bag} = 0.375 \times \text{Mass} + 50$$