Use the image to answer the question.
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
To determine the constant of proportionality, we need to use the given information. In this case, we know that the cost of ice cream custard is directly proportional to its weight in ounces. This means that the equation will have the form y = kx, where y is the cost of the custard, x is the weight in ounces, and k is the constant of proportionality.
Now, let's look at the graph provided. We can see that both the x-axis and the y-axis represent the weight in ounces and the cost of the custard, respectively. From the graph, we can identify two points: (0, 0) and (5, 5).
Using the point (0, 0), we can substitute the values into the equation y = kx:
0 = k * 0
Simplifying, we get:
0 = 0
This equation is true for any value of k since any number multiplied by zero is zero. Therefore, we cannot determine the value of k from this equation.
Using the point (5, 5), we can substitute the values into the equation y = kx:
5 = k * 5
Simplifying, we get:
5 = 5k
Dividing both sides of the equation by 5, we find:
k = 1
Therefore, the constant of proportionality for this graph is 1. The equation of the graph is y = x.
To find the equation of the graph, we need to determine the constant of proportionality. Since the cost of ice cream custard is directly proportional to its weight, we know that the equation will be in the form y = kx, where k represents the constant of proportionality.
To determine the value of k, we can look at the image provided. By examining the graph, we can identify a point where the cost and weight intersect. Let's say that point is (2, 2), meaning the weight of the ice cream custard is 2 ounces and its cost is also 2 units (dollars, for example).
Since we know that y = kx, we can plug in the values from the point into the equation: 2 = k * 2. Now we can solve for k:
2 = k * 2
Divide both sides by 2:
1 = k
Thus, the constant of proportionality, or the value of k, is 1. Therefore, the complete equation of the graph is y = x.