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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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Remaining Attempts : 3
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Answer 1

To find the equation of the graph representing the relationship between weight and cost, we can use the formula for direct proportionality:

\[ C = k \cdot W \]

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

From the graph, we can see that the line passes through the point \( (2, 10) \). This means that when the weight \( W = 2 \) ounces, the cost \( C = 10 \) dollars.

Now we can substitute the values of \( C \) and \( W \) into the equation to solve for \( k \):

\[ 10 = k \cdot 2 \]

To find \( k \), we divide both sides by 2:

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

Now that we have the constant of proportionality \( k \), we can write the complete equation as:

\[ C = 5W \]

Thus, the equation of the graph with its constant of proportionality is:

\[ C = 5W \]