Consider the table.

Question

length(X) weight (Y)
6 15
9 22.5
12 30
15 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

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Answer 1

The relationship between the length (X) and weight (Y) of the pet ferret is a direct variation, which means that the weight is proportional to the length.

To find the constant of proportionality (k), we can use any of the pairs of values from the table. The formula for direct variation can be expressed as:

\[ Y = k \cdot X \]

Let's use the first pair (length = 6, weight = 15):

\[ k = \frac{Y}{X} = \frac{15}{6} = 2.5 \]

So, the constant of proportionality is \( 2.5 \).

Now, to write the equation that relates Y and X, we replace \( k \) with \( 2.5 \):

\[ Y = 2.5 \cdot X \]

Thus, the equation may be expressed as:

\[ y = 2.5x \]