To determine the constant of proportionality for each scenario and the corresponding point, we need to analyze the relationships described.
-
Eggs used per batch of cookies:
- Let's assume the relationship is linear, meaning that the number of eggs increases uniformly with the number of batches of cookies.
- If we have the ratio of eggs (y) to batches (x), we can express this as \( k = \frac{y}{x} \).
- For instance, if for 1 batch (x = 1), 2 eggs (y = 2) are used, \( k = \frac{2}{1} = 2 \). Therefore, the constant of proportionality is 2 eggs per batch and the point representing this relationship is (1, 2).
-
Per peach:
- If the cost per peach is a fixed ratio, for example, $3 for 1 peach, we can express this as \( k = \frac{y}{x} \) where \( y \) is the total cost and \( x \) is the number of peaches.
- In this case, when \( x = 1 \) (for one peach), \( y = 3 \). Thus, the constant of proportionality is 3 per peach and the point that represents this constant is (1, 3).
-
Markers per package:
- Assuming each package contains a fixed number of markers, such as 10 markers per package, we can set \( k = \frac{y}{x} \).
- If \( x = 1 \) (one package), then \( y = 10 \). Thus, the constant of proportionality is 10 markers per package and the point representing this relationship is (1, 10).
-
Blue beads per red bead:
- If there are, for example, ½ blue beads for every red bead (indicating a ratio), we could use this example to illustrate the point.
- Therefore, if \( x = 1 \) (one red bead), \( y = ½ \). The constant of proportionality would be \(\frac{1}{2}\), and the point representing this relationship is (1, ½).
In summary:
- Eggs used per batch: 2 (1, 2)
- Per peach: 3 (1, 3)
- Markers per package: 10 (1, 10)
- Blue beads per red bead: \(\frac{1}{2}\) (1, \(\frac{1}{2}\))