Use the image to answer the question.

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

To find the equation that represents the relationship shown in the graph, we follow the formula for direct proportionality:

\[ \text{Cost} = k \times \text{Weight} \]

Where \( k \) is the constant of proportionality. From the information given, we see that the line passes through the point (2, 10), which means when the weight is 2 ounces, the cost is 10 dollars.

Now we can use this point to find \( k \):

\[ 10 = k \times 2 \]

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

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

Now we can complete the equation with the found constant of proportionality:

\[ \text{Cost} = 5 \times \text{Weight} \]

Thus, the completed equation is:

Cost = 5 × Weight