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Question

A graph shows the x-axis representing weight in ounces ranging from 0 to 6 in increments of 2, and the y-axis representing cost in dollars ranging from 0 to 15 in increments of 5. A line is drawn ending with an arrow. The line begins at the origin and passes through left parenthesis 2 comma 10 right parenthesis.
At the Custard Creamery, the cost of ice cream custard is directly proportional to its weight in ounces. Complete the equation of the graph with its constant of proportionality.

(1 point)
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Answer 1

The relationship between the cost \( C \) and the weight \( w \) in ounces can be expressed as:

\[ C = k \cdot w \]

where \( k \) is the constant of proportionality.

From the graph, we see that the line passes through the point \( (2, 10) \). This means that when the weight \( w = 2 \) ounces, the cost \( C = 10 \) dollars. We can use this point to find the constant \( k \).

Substituting the values into the equation:

\[ 10 = k \cdot 2 \]

To solve for \( k \), we can rearrange the equation:

\[ k = \frac{10}{2} = 5 \]

Thus, the constant of proportionality is \( 5 \). Therefore, the complete equation of the graph is:

\[ C = 5w \]

This shows that the cost of ice cream custard at the Custard Creamery is directly proportional to its weight, with a constant of proportionality of 5 dollars per ounce.