The price for footballs is displayed in the graph, derive the equation of the proportional relationship through the origin

Answer 1

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.