The price for footballs is displayed in the graph.
Derive the equation of the proportional relation
through the origin.
graph shows, 5 dots, 1 dot is over 4 across from 36, 2 dot is over 3 across from 27, 3 dot is over 2 across from 18, 4 dot is over 1 across from 9 and 5 dot is over 0 across from 0
To find the equation of the proportional relation through the origin, we need to determine the ratio between the number of footballs and their price.
Let's denote the number of footballs as "x" and their price as "y". In this case, we have the following data points from the graph:
(4, 36), (3, 27), (2, 18), (1, 9), (0, 0)
We can see that as the number of footballs decreases, their price also decreases. This indicates a proportional relationship.
Now, let's calculate the ratio between the number of footballs and their price for each data point:
For the first data point: x/y = 4/36 = 1/9
For the second data point: x/y = 3/27 = 1/9
For the third data point: x/y = 2/18 = 1/9
For the fourth data point: x/y = 1/9 = 1/9
For the fifth data point: x/y = 0/0 (Undefined)
We can observe that the ratio x/y is constant for the first four data points, which implies a proportional relationship. Thus, the equation of the proportional relation through the origin is:
x/y = 1/9
Alternatively, if we cross multiply the ratio, we have:
x * 9 = y
Therefore, the equation of the proportional relation through the origin is y = 9x.