The price for footballs is displayed in the graph. Derive the equation of the proportional relationship through the origin.
To derive the equation of the proportional relationship through the origin, we need to find the slope of the line represented by the graph.
Looking at the graph, we can see that the price (P) is on the y-axis and the number of footballs (N) is on the x-axis. The line passes through the origin, indicating that the relationship is proportional.
The slope of the line represents the rate of change of the price with respect to the number of footballs. In other words, it tells us how much the price changes for each additional football.
To find the slope, we can choose two points on the line and calculate the rise over run.
Let's choose the points (0, 0) and (4, 32) from the graph.
Rise = Change in y-values = 32 - 0 = 32
Run = Change in x-values = 4 - 0 = 4
Slope = Rise/Run = 32/4 = 8
Therefore, the slope of the line is 8.
Since the relationship is proportional and passes through the origin, the equation of the line can be written as:
P = kN
Where P represents the price, N represents the number of footballs, and k is the constant of proportionality.
From the slope, we know that k = 8.
Hence, the equation of the proportional relationship through the origin is:
P = 8N
In order to derive the equation of the proportional relationship through the origin, we need to determine the relationship between the price of footballs and the quantity.
From the graph, we can observe that as the quantity of footballs increases, the price also increases, but it passes through the origin (0,0).
A proportional relationship can be expressed using the equation y = kx, where y represents the dependent variable (price), x represents the independent variable (quantity), and k is the constant of proportionality.
Since the relationship passes through the origin, the equation becomes y = kx, where k represents the constant of proportionality.
Therefore, the equation of the proportional relationship through the origin for the price of footballs can be expressed as y = kx.
To derive the equation of the proportional relationship through the origin, we need to determine the relationship between the price of footballs and the corresponding quantity or number of footballs.
First, let's take a look at the graph that displays the price for footballs. Identify two points on the graph that lie on a straight line passing through the origin (0,0). Note the coordinates of these two points, which will give us the values for the quantity of footballs and their corresponding prices.
For example, let's say we have two points: (2, $10) and (4, $20). This means that when there are 2 footballs, the price is $10, and when there are 4 footballs, the price is $20.
Now we can determine the ratio between the quantity of footballs and their corresponding prices. In this case, the ratio is 2:10 and 4:20, which simplifies to 1:5.
Since the relationship is proportional through the origin, we can represent it using the equation y = kx, where y is the price of footballs, x is the quantity of footballs, and k is the constant of proportionality.
Using one of the points on the graph, (2, $10), we can substitute these values into the equation to determine the value of k:
$10 = k * 2
Solving for k, we find that k is 5.
Therefore, the equation of the proportional relationship through the origin is y = 5x.
This equation means that for every additional football, the price increases by $5.