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.

Answer 1

Since the cost of ice cream custard is directly proportional to its weight in ounces, we can express this relationship with the equation:

\[ C = k \cdot W \]

where \( C \) represents the cost in dollars, \( W \) represents the weight in ounces, and \( k \) is the constant of proportionality.

From the information provided, the line passes through the point (2, 10). This means that when the weight \( W \) is 2 ounces, the cost \( C \) is 10 dollars.

We can substitute these values into the equation to find the constant of proportionality \( k \):

\[
10 = k \cdot 2
\]

To solve for \( k \), divide both sides by 2:

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

Now we can write the complete equation that represents the cost of ice cream custard:

\[
C = 5W
\]

Thus, the constant of proportionality is \( k = 5 \).