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.
Answers
GPT-4o mini
To determine the equation of the graph representing the cost of ice cream custard at the Custard Creamery, we start by noting that the cost (\(C\)) is directly proportional to the weight (\(W\)) in ounces. This relationship can be expressed mathematically as:
\[
C = k \cdot W
\]
where \(k\) is the constant of proportionality.
Given that the line passes through the point \( (2, 10) \), we can use this point to find the value of \(k\). Here, \(W = 2\) ounces and \(C = 10\) dollars.
Substituting these values into the equation gives:
\[
10 = k \cdot 2
\]
To solve for \(k\), divide both sides by 2:
\[
k = \frac{10}{2} = 5
\]
Now, we have found the constant of proportionality \(k = 5\). Therefore, the complete equation relating the cost of the ice cream custard to its weight in ounces is:
\[
C = 5W
\]
In summary, the equation is \(C = 5W\), with a constant of proportionality \(k = 5\).
\[
C = k \cdot W
\]
where \(k\) is the constant of proportionality.
Given that the line passes through the point \( (2, 10) \), we can use this point to find the value of \(k\). Here, \(W = 2\) ounces and \(C = 10\) dollars.
Substituting these values into the equation gives:
\[
10 = k \cdot 2
\]
To solve for \(k\), divide both sides by 2:
\[
k = \frac{10}{2} = 5
\]
Now, we have found the constant of proportionality \(k = 5\). Therefore, the complete equation relating the cost of the ice cream custard to its weight in ounces is:
\[
C = 5W
\]
In summary, the equation is \(C = 5W\), with a constant of proportionality \(k = 5\).