the question
Cost (5)
15-
10-
5-
0
0
2
4
6
Weight (in ounces)
At the Custard Creamery, the cost of ice cream custard is directly proportional to ts weight in ounces. Complete the equation of the graph with its constant of proportionality
J = Box x
To find the constant of proportionality, we can use any pair of corresponding values from the table. Let's choose the first pair, where the cost is $15 and the weight is 5 ounces.
We can set up the equation as follows:
15 = Box x 5
To isolate the constant of proportionality (Box), divide both sides of the equation by 5:
Box = 15 / 5
Simplifying the equation gives us:
Box = 3
Therefore, the constant of proportionality is 3.
The equation can be written as J = Box x, where J represents the cost of ice cream custard and x represents the weight in ounces. To find the constant of proportionality (Box), we can use the given data points.
Let's take the first data point, where the cost is 15 and the weight is 5. Plugging these values into the equation, we get:
15 = Box x 5
Next, let's take the second data point, where the cost is 10 and the weight is 10. Plugging these values into the equation, we get:
10 = Box x 10
Simplifying both equations, we have:
15 = 5Box
10 = 10Box
Now, we can solve these equations simultaneously to find the value of Box.
From the second equation, we can divide both sides by 10:
1 = Box
Now, substituting this value of Box into either of the equations, we get:
15 = 5Box
15 = 5(1)
15 = 5
Therefore, the constant of proportionality (Box) is 1.
The equation of the graph is J = x
To complete the equation of the graph, we need to determine the constant of proportionality between the cost and weight of the ice cream custard.
The given data shows the cost (J) and weight (Box) of the ice cream custard:
Cost (J):
15-
10-
5-
0
0
2
4
6
Weight (Box) (in ounces):
5-
0
0
2
4
6
To find the constant of proportionality, we can choose any two data points and use the formula for proportionality:
Constant of Proportionality = Cost (J) / Weight (Box)
Let's select the data points (5, 15) and (2, 4) to calculate the constant of proportionality:
For the first data point (5, 15):
Constant of Proportionality = Cost (15) / Weight (5) = 15/5 = 3
For the second data point (2, 4):
Constant of Proportionality = Cost (4) / Weight (2) = 4/2 = 2
Since the constant of proportionality should be the same for all data points, we can take the average of the two calculated values:
Average Constant of Proportionality = (3 + 2) / 2 = 5/2 = 2.5
Therefore, the equation of the graph with its constant of proportionality is:
J = 2.5 x Box
Hence, the equation is J = 2.5x.