At the Custard Creamery, the cost of ice cream custard is directly proportional to its weight in ounces. At the Custard Creamery, the cost of ice cream custard is directly proportional to its weight in ounces.
o (2,6)
o (3/2, 3)
o (2/3 4)
o (1/4, 2)
The correct answer is: (3/2, 3)
To determine which equation represents a direct proportion relationship between the weight of the ice cream custard and its cost in ounces, we can examine the given options.
Option 1: (2,6)
Option 2: (3/2, 3)
Option 3: (2/3, 4)
Option 4: (1/4, 2)
In a direct proportion, if the weight (x) increases, the cost (y) should also increase proportionally.
Let's calculate the unit rate (constant of proportionality) for each option by dividing the cost by the weight:
Option 1: 6/2 = 3
Option 2: 3/ (3/2) = 2
Option 3: 4/ (2/3) = 6
Option 4: 2/ (1/4) = 8
The unit rate (constant of proportionality) should remain constant for a direct proportion. Therefore, the correct direct proportion relationship is represented by the option with a constant unit rate.
From the calculations, we can see that Option 2: (3/2, 3) has a constant unit rate of 2. Hence, the equation that represents the direct proportion relationship between the weight of the ice cream custard and its cost in ounces is:
Cost = (Weight) * 2
Therefore, option 2: (3/2, 3) represents the correct direct proportion relationship.
To determine if the given points represent a direct variation relationship between the cost of ice cream custard and its weight in ounces, we need to check if they satisfy the conditions for direct variation.
In direct variation, two variables are directly proportional if they can be written in the form y = kx, where y is the dependent variable, x is the independent variable, and k is the constant of variation.
Let's check each set of points to see if they follow this pattern:
1. (2, 6)
The equation form would be y = kx.
Plugging in the values, we get 6 = k * 2.
Dividing both sides by 2, we get k = 3.
Therefore, the equation for this set of points is y = 3x.
2. (3/2, 3)
The equation form would be y = kx.
Plugging in the values, we get 3 = k * (3/2).
Simplifying the equation, we get 3 = (3/2)k.
Multiplying both sides by 2/3, we get k = 2.
Therefore, the equation for this set of points is y = 2x.
3. (2/3, 4)
The equation form would be y = kx.
Plugging in the values, we get 4 = k * (2/3).
Simplifying the equation, we get 4 = (2/3)k.
Multiplying both sides by 3/2, we get k = 6/2 = 3.
Therefore, the equation for this set of points is y = 3x.
4. (1/4, 2)
The equation form would be y = kx.
Plugging in the values, we get 2 = k * (1/4).
Simplifying the equation, we get 2 = (1/4)k.
Multiplying both sides by 4, we get k = 8.
Therefore, the equation for this set of points is y = 8x.
After analyzing all the sets of points, we can see that only the first set (2, 6) satisfies the conditions for direct variation. Therefore, the correct answer is (2, 6).