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)

User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
15 days ago

To determine the equation of the line that represents the relationship between weight (x) and cost (y) for the ice cream custard, we start with the relationship given by the direct proportionality.

The equation can be written in the form:

\[ y = kx \]

where \( k \) is the constant of proportionality.

From the graph, we see that the line passes through the point \( (2, 10) \). This gives us the values of \( x \) (weight in ounces) and \( y \) (cost in dollars). We can use this point to calculate \( k \):

1. Substitute \( x = 2 \) and \( y = 10 \) into the equation:

\[ 10 = k \cdot 2 \]

2. Solve for \( k \):

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

Thus, the constant of proportionality \( k \) is 5.

The complete equation describing the relationship between weight and cost is:

\[ y = 5x \]