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

Answer 1

Since the cost of ice cream custard is directly proportional to its weight, we can express this relationship with the equation:

\[ y = kx \]

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

To determine the value of \( k \), we can look at the graph's coordinates. For example, if at 2 ounces (where \( x = 2 \)), the cost (where \( y = 5 \)), we can substitute these values into the equation:

\[ 5 = k \cdot 2 \]

Now solve for \( k \):

\[ k = \frac{5}{2} = 2.5 \]

So the equation becomes:

\[ y = 2.5x \]

Thus, the complete equation is:

\[ y = 2.5x \]