The constant of proportionality is the amount a relationship will change for each unit.

It is represented by the value of this ratio: k=yx

One of the ways a proportional relationship is identified is with a graph.

Notice the graph will show a straight line that extends through the origin. The ratio of each point is equivalent.

Point A: (12, 4) k=yx=412=13

Point B: (24, 8) k=yx=824=13

Point C: (36, 12) k=yx=1236=13

The constant of proportionality for this relationship is 13
download per web visit.

The point that represents the constant of proportionality is (1, 13
).

(8 points)
Determine the constant of proportionality for each graph and the point that represents the constant of proportionality.

The constant of proportionality is
eggs used per batch of cookies. and the point that represents the constant of proportionality is (
).

================================



The constant of proportionality is $
per peach and the point that represents the constant of proportionality is (
). **Enter your answer as decimal.**

================================

The constant of proportionality is
markers per package and the point that represents the constant of proportionality is (
).

================================

The constant of proportionality is
blue beads per red bead and the point that represents the constant of proportionality is (
). **Enter your answer as a fraction.**

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1 answer

To determine the constant of proportionality and the corresponding point that represents it, we can follow the process you've outlined. Here are some examples based on the format you've provided:

  1. Eggs used per batch of cookies: Let's say after analyzing a graph or data, we find that there are 2 eggs used per batch. Therefore, the constant of proportionality is 2, and the corresponding point that represents this constant is (1, 2).

    Answer: The constant of proportionality is 2 eggs used per batch of cookies, and the point that represents the constant of proportionality is (1, 2).

  2. Dollars per peach: If each peach costs $0.75, the constant of proportionality is 0.75, and the corresponding point is (1, 0.75).

    Answer: The constant of proportionality is 0.75 per peach, and the point that represents the constant of proportionality is (1, 0.75).

  3. Markers per package: Assume that there are 5 markers in each package; thus, the constant of proportionality is 5, represented by the point (1, 5).

    Answer: The constant of proportionality is 5 markers per package, and the point that represents the constant of proportionality is (1, 5).

  4. Blue beads per red bead: Suppose the constant of proportionality is 3 blue beads for every red bead. In fractional terms, this would be expressed as \( \frac{3}{1} \) (3 blue beads per red bead), and the corresponding point is (1, 3).

    Answer: The constant of proportionality is 3 blue beads per red bead, and the point that represents the constant of proportionality is (1, \frac{3}{1}).

Feel free to replace the values with those specific to your scenario or to adjust these examples based on the specific graphs or data you have!

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