Bot GPT 4-o mini To derive the equation of the proportional relationship shown in the graph, we can observe the coordinates plotted on the graph:
- At 0 footballs, the cost is 0: (0, 0)
- At 1 football, the cost is 9: (1, 9)
- At 2 footballs, the cost is 18: (2, 18)
- At 3 footballs, the cost is 27: (3, 27)
- At 4 footballs, the cost is 36: (4, 36)
From these points, we see that as the quantity of footballs increases, the cost increases proportionally.
The relationship appears to be linear, and we can express it in the form of the equation:
\[ \text{Cost} = k \times \text{Quantity} \]
To find the constant of proportionality \( k \), we can use any of the given points. Let's use the point (1, 9):
\[ 9 = k \times 1 \] \[ k = 9 \]
Thus, the equation of the proportional relationship is:
\[ \text{Cost} = 9 \times \text{Quantity} \]
This means the cost for each football is $9.