To derive the equation of the proportional relationship presented in the graph, we need to identify the relationship between the quantity of footballs and their corresponding costs.
From the points provided:
- When Quantity = 0, Cost = 0
- When Quantity = 1, Cost = 9
- When Quantity = 2, Cost = 18
- When Quantity = 3, Cost = 27
- When Quantity = 4, Cost = 36
We can observe that the cost increases by 9 for each additional football purchased. Hence, the relationship can be described as a linear equation of the form:
\[ \text{Cost} = k \times \text{Quantity} \]
Here, \( k \) is the constant of proportionality. From the points given, we can find \( k \):
When Quantity = 1, Cost = 9: \[ k = \frac{\text{Cost}}{\text{Quantity}} = \frac{9}{1} = 9 \]
Thus, the equation that represents this proportional relationship is:
\[ \text{Cost} = 9 \times \text{Quantity} \]
This is the equation derived from the graph.