To derive the equation of the proportional relationship through the origin, we first observe the points plotted on the graph. The points given are:
- (0, 0)
- (1, 9)
- (2, 18)
- (3, 27)
- (4, 36)
From these points, we can see that the cost increases by 9 for each additional football bought.
The relationship can be expressed in the form:
\[ \text{Cost} = k \times \text{Quantity} \]
where \( k \) is the constant of proportionality.
To find \( k \), we can use one of the points from the graph. Using the point (1, 9):
\[ 9 = k \times 1 \]
From this, we find:
\[ k = 9 \]
Now, we can write the equation of the proportional relationship:
\[ \text{Cost} = 9 \times \text{Quantity} \]
So the equation that represents the cost of the footballs is:
\[ \text{Cost} = 9Q \]
where \( Q \) is the quantity of footballs.