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.

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)
y=
x
Remaining Attempts : 3
Skip to navigation

Answer 1

To find the equation for the relationship described, we can use the general form of a direct variation equation, which is:

\[ y = kx \]

where \( y \) is the cost, \( x \) is the weight in ounces, and \( k \) is the constant of proportionality.

Based on the information provided, we have the following points from the graph:

1. When \( x = 2 \) ounces, assume \( y \) could be inferred from the graph, let's say \( y = 5 \) dollars (an example; you'll need to confirm this from your graph).
2. When \( x = 4 \) ounces, assume \( y = 10 \) dollars (again, please confirm).

Using the first point:

• When \( x = 2 \), \( y = 5 \): \[ 5 = k \cdot 2 \] \[ k = \frac{5}{2} = 2.5 \]

Now you can use the constant of proportionality calculated:

• Thus the equation becomes: \[ y = 2.5x \]

Make sure you check the values from the graph to confirm the constant of proportionality is correct.

Final answer: \[ y = 2.5x \]

Answer 2

Wrong

Answer 3

I apologize for the confusion. Let's reevaluate the information step by step.

Given Information:

• The x-axis represents weight in ounces (0 to 6 in increments of 2).
• The y-axis represents cost in dollars (0 to 15 in increments of 5).
• The cost of ice cream custard is directly proportional to its weight.

Understanding the Graph:

1. Identify specific points on the graph. If you have values from the graph, such as:
   • For example, if at \( x = 0 \), \( y = 0 \) (the starting point),
   • At \( x = 2 \), suppose \( y = 5 \) (or whatever point you want to take),
   • At \( x = 4 \), suppose \( y = 10 \),
   • At \( x = 6 \), suppose \( y = 15 \).

Analyzing the Points:

Let’s use the values to find the constant of proportionality \( k \):

• When \( x = 2\), \( y = 5 \): \[ 5 = k \cdot 2 \implies k = \frac{5}{2} = 2.5 \]

• If you check other points, for \( x = 4\), \( y = 10 \): \[ 10 = k \cdot 4 \implies k = \frac{10}{4} = 2.5 \]

• Similarly, for \( x = 6\), \( y = 15 \): \[ 15 = k \cdot 6 \implies k = \frac{15}{6} = 2.5 \]

Conclusion:

If the points on the graph do indeed follow the proportional values like these, the constant of proportionality \( k \) consistently equals \( 2.5 \).

The equation is still: \[ y = 2.5x \] However, if this is not correct according to the points you were given, could you please specify the exact points shown in your graph? That way, I can help derive the proper equation from the exact data. Thank you!