Question
Football cost
Cost y
Quantity x
Dot 2 1,9
Dot 3 3,27
Dot 4 4,36
Dot 5 5,48
The price for footballs is displayed in the graph. Devere the equation of the propositional relationship through the origin
Cost y
Quantity x
Dot 2 1,9
Dot 3 3,27
Dot 4 4,36
Dot 5 5,48
The price for footballs is displayed in the graph. Devere the equation of the propositional relationship through the origin
Answers
GPT-4o mini
To derive the equation of the proportional relationship through the origin, we first need to determine the relationship between the cost \( y \) and the quantity \( x \) of footballs.
From the data provided:
- Dot 2: \( (1.9, 2) \)
- Dot 3: \( (3.27, 3) \)
- Dot 4: \( (4.36, 4) \)
- Dot 5: \( (5.48, 5) \)
To find the equation of a proportional relationship in the form \( y = kx \), where \( k \) is the constant of proportionality, we can calculate \( k \) for each point using the formula:
\[
k = \frac{y}{x}
\]
Calculating \( k \) for each dot:
1. For \( (2, 1.9) \):
\[
k = \frac{1.9}{2} = 0.95
\]
2. For \( (3, 3.27) \):
\[
k = \frac{3.27}{3} = 1.09
\]
3. For \( (4, 4.36) \):
\[
k = \frac{4.36}{4} = 1.09
\]
4. For \( (5, 5.48) \):
\[
k = \frac{5.48}{5} = 1.096
\]
It seems that the value of \( k \) is not consistent across all points, which implies the relationship is not perfectly proportional. However, we can use the average of the calculated \( k \) values to find an approximate relationship.
Calculating the average \( k \):
\[
k \approx \frac{0.95 + 1.09 + 1.09 + 1.096}{4} = \frac{4.233}{4} \approx 1.05825
\]
Thus, we can generally express the relationship using the equation:
\[
y \approx 1.06x
\]
This equation represents the approximate linear relationship between the cost and the quantity of footballs, assuming a proportional relationship through the origin.
From the data provided:
- Dot 2: \( (1.9, 2) \)
- Dot 3: \( (3.27, 3) \)
- Dot 4: \( (4.36, 4) \)
- Dot 5: \( (5.48, 5) \)
To find the equation of a proportional relationship in the form \( y = kx \), where \( k \) is the constant of proportionality, we can calculate \( k \) for each point using the formula:
\[
k = \frac{y}{x}
\]
Calculating \( k \) for each dot:
1. For \( (2, 1.9) \):
\[
k = \frac{1.9}{2} = 0.95
\]
2. For \( (3, 3.27) \):
\[
k = \frac{3.27}{3} = 1.09
\]
3. For \( (4, 4.36) \):
\[
k = \frac{4.36}{4} = 1.09
\]
4. For \( (5, 5.48) \):
\[
k = \frac{5.48}{5} = 1.096
\]
It seems that the value of \( k \) is not consistent across all points, which implies the relationship is not perfectly proportional. However, we can use the average of the calculated \( k \) values to find an approximate relationship.
Calculating the average \( k \):
\[
k \approx \frac{0.95 + 1.09 + 1.09 + 1.096}{4} = \frac{4.233}{4} \approx 1.05825
\]
Thus, we can generally express the relationship using the equation:
\[
y \approx 1.06x
\]
This equation represents the approximate linear relationship between the cost and the quantity of footballs, assuming a proportional relationship through the origin.