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.
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.
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 establish the equation representing the relationship between weight and cost in this context, we can start with the formula that illustrates direct proportionality. The equation can be expressed as:
\[
C = k \cdot W
\]
Where:
- \( C \) is the cost in dollars,
- \( W \) is the weight in ounces,
- \( k \) is the constant of proportionality.
From the description provided, we can analyze the points on the graph. Let's assume a typical case scenario based on the increments mentioned (although we need an actual point to get the constant of proportionality):
If, for example, the cost of 2 ounces of custard is $5, we can substitute these values into the equation to find \( k \):
\[
5 = k \cdot 2
\]
Solving for \( k \):
\[
k = \frac{5}{2} = 2.5
\]
Thus, the equation relating the cost \( C \) to the weight \( W \) will be:
\[
C = 2.5 W
\]
This means for every ounce of ice cream custard purchased, the cost increases by $2.50. Adjust or apply specific values if your graph data points differ, but the methodology will remain the same.
\[
C = k \cdot W
\]
Where:
- \( C \) is the cost in dollars,
- \( W \) is the weight in ounces,
- \( k \) is the constant of proportionality.
From the description provided, we can analyze the points on the graph. Let's assume a typical case scenario based on the increments mentioned (although we need an actual point to get the constant of proportionality):
If, for example, the cost of 2 ounces of custard is $5, we can substitute these values into the equation to find \( k \):
\[
5 = k \cdot 2
\]
Solving for \( k \):
\[
k = \frac{5}{2} = 2.5
\]
Thus, the equation relating the cost \( C \) to the weight \( W \) will be:
\[
C = 2.5 W
\]
This means for every ounce of ice cream custard purchased, the cost increases by $2.50. Adjust or apply specific values if your graph data points differ, but the methodology will remain the same.