Question
Consider the table.
Length(x) 6 9 12 15
Weight(y) 15 22.5 30 37.5
The weight of the pet ferret varies directly with its length.
(1 point)
The constant of proportionality is
.
The following equation may be used to determine the weight of ferret given its length:
y =
x
Length(x) 6 9 12 15
Weight(y) 15 22.5 30 37.5
The weight of the pet ferret varies directly with its length.
(1 point)
The constant of proportionality is
.
The following equation may be used to determine the weight of ferret given its length:
y =
x
Answers
GPT-4o mini
To find the constant of proportionality and the equation relating length (x) and weight (y), we can look at the provided data.
The relationship is described as "varies directly," which means we can express it as:
\[ y = kx \]
where \( k \) is the constant of proportionality.
We can calculate \( k \) using the provided values. Taking one of the pairs, for instance \( x = 6 \) and \( y = 15 \):
\[ 15 = k \cdot 6 \]
To find \( k \):
\[ k = \frac{15}{6} = 2.5 \]
We can check this with other pairs:
1. For \( x = 9 \) and \( y = 22.5 \):
\[ 22.5 = k \cdot 9 \]
\[ k = \frac{22.5}{9} = 2.5 \]
2. For \( x = 12 \) and \( y = 30 \):
\[ 30 = k \cdot 12 \]
\[ k = \frac{30}{12} = 2.5 \]
3. For \( x = 15 \) and \( y = 37.5 \):
\[ 37.5 = k \cdot 15 \]
\[ k = \frac{37.5}{15} = 2.5 \]
Since \( k \) is consistently \( 2.5 \) across all pairs, we find:
The constant of proportionality is **2.5**.
Now, we can write the equation using the constant of proportionality:
\[ y = 2.5x \]
So, the final answer is:
The constant of proportionality is **2.5**.
The equation may be used to determine the weight of the ferret given its length:
\( y = 2.5x \).
The relationship is described as "varies directly," which means we can express it as:
\[ y = kx \]
where \( k \) is the constant of proportionality.
We can calculate \( k \) using the provided values. Taking one of the pairs, for instance \( x = 6 \) and \( y = 15 \):
\[ 15 = k \cdot 6 \]
To find \( k \):
\[ k = \frac{15}{6} = 2.5 \]
We can check this with other pairs:
1. For \( x = 9 \) and \( y = 22.5 \):
\[ 22.5 = k \cdot 9 \]
\[ k = \frac{22.5}{9} = 2.5 \]
2. For \( x = 12 \) and \( y = 30 \):
\[ 30 = k \cdot 12 \]
\[ k = \frac{30}{12} = 2.5 \]
3. For \( x = 15 \) and \( y = 37.5 \):
\[ 37.5 = k \cdot 15 \]
\[ k = \frac{37.5}{15} = 2.5 \]
Since \( k \) is consistently \( 2.5 \) across all pairs, we find:
The constant of proportionality is **2.5**.
Now, we can write the equation using the constant of proportionality:
\[ y = 2.5x \]
So, the final answer is:
The constant of proportionality is **2.5**.
The equation may be used to determine the weight of the ferret given its length:
\( y = 2.5x \).