The price for footballs is displayed in the graph, derive the equation of the proportional relationship through the origin
In a proportional relationship, the equation can be written in the form y = kx, where k is the constant of proportionality.
Looking at the graph, we can see that the line passes through the origin. This means that when the price is $0, the number of footballs is also 0.
From the graph, we can see that the price for 5 footballs is $40. This gives us a data point of (5, 40).
Substitute this point into the equation y = kx:
40 = k(5)
Solving for k:
40 = 5k
k = 40/5
k = 8
Therefore, the equation of the proportional relationship through the origin is:
y = 8x
This means that the price of footballs is 8 times the number of footballs purchased.