he price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin.
graph proportions; (1,9), (2,18), (3,27) and (4,36)
To derive the equation of the proportional relationship through the origin from the given graph proportions, we need to find the constant ratio between the x-values and the y-values.
Let's take the first set of points: (1,9).
The x-value is 1, and the y-value is 9.
Similarly, for the second set of points: (2,18).
The x-value is 2, and the y-value is 18.
We can observe that when the x-values are doubled, the y-values are also doubled. This indicates a linear proportional relationship.
Now, we can calculate the constant ratio by dividing the y-values by the x-values:
For the first set of points: 9/1 = 9.
For the second set of points: 18/2 = 9.
Since the constant ratio is the same for both sets, we can conclude that the equation of the proportional relationship is y = 9x.
Therefore, the equation of the proportional relationship through the origin is y = 9x.
To derive the equation of the proportional relationship through the origin, we need to find the constant of proportionality.
In this case, the graph represents the relationship between the number of footballs (x-axis) and their corresponding prices (y-axis). Since we are looking for a proportional relationship through the origin, it means that when the number of footballs is 0, the price of the footballs will also be 0.
Let's examine the points given: (1,9), (2,18), (3,27), and (4,36).
If we divide the y-coordinate (price) by the x-coordinate (number of footballs), we can check if there is a constant ratio between them.
For the point (1,9), 9 divided by 1 equals 9.
For the point (2,18), 18 divided by 2 equals 9.
For the point (3,27), 27 divided by 3 equals 9.
For the point (4,36), 36 divided by 4 equals 9.
Since the ratio of the y-coordinate divided by the x-coordinate is consistently 9, we can conclude that the constant of proportionality is 9.
Thus, the equation of the proportional relationship through the origin can be written as y = 9x.
To find the equation of the proportional relationship through the origin, we need to find the constant of proportionality, which is the ratio of the y-values to the x-values for any two points on the graph.
Let's consider the points (1,9) and (2,18). The ratio of the y-values to the x-values is 18/9 = 2/1 = 2.
Similarly, for the points (2,18) and (3,27), the ratio of the y-values to the x-values is 27/18 = 3/2 = 1.5.
Finally, for the points (3,27) and (4,36), the ratio of the y-values to the x-values is 36/27 = 4/3 = 1.33.
Since the ratios are not the same for the different point pairs, it means that the relationship is not directly proportional. Therefore, there is no equation of the proportional relationship through the origin for this graph.