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The given table represents the number of items purchased and the total cost.

A table showing number of items and total cost. Two items cost seven dollars. Four items cost 14 dollars. Six items cost 21 dollars. And eight items cost 28 dollars.

Part A

Select all of the statements which describe the relationship between these two quantities.

The ratios in this table are not equivalent.


The ratios in this table are equivalent.


The two quantities in this table represent a proportional relationship.


The two quantities in this table do not represent a proportional relationship.


The graph of this relationship would be a straight line through the origin.
Part B

Identify the constant of proportionality.

1 answer

Part A

Let's analyze the statements:

  1. The ratios in this table are not equivalent.

    • False. The ratios (cost to items) are equivalent—each two items costs $7, which simplifies to \( \frac{7}{2} = 3.5 \) dollars per item.

  2. The ratios in this table are equivalent.

    • True. Each ratio of total cost to the number of items purchased equals 3.5.

  3. The two quantities in this table represent a proportional relationship.

    • True. Since the ratios are equivalent, they form a proportional relationship.

  4. The two quantities in this table do not represent a proportional relationship.

    • False. The quantities do represent a proportional relationship.

  5. The graph of this relationship would be a straight line through the origin.

    • True. A proportional relationship will graph as a straight line through the origin (0,0).

Summary for Part A:

  • True statements:
    • The ratios in this table are equivalent.
    • The two quantities in this table represent a proportional relationship.
    • The graph of this relationship would be a straight line through the origin.

Part B

To find the constant of proportionality (k), we can use the ratio of total cost to the number of items. The ratio is calculated by taking the total cost and dividing by the number of items:

For example:

  • From the first entry, \( k = \frac{7}{2} = 3.5 \)
  • From the second entry, \( k = \frac{14}{4} = 3.5 \)
  • From the third entry, \( k = \frac{21}{6} = 3.5 \)
  • From the fourth entry, \( k = \frac{28}{8} = 3.5 \)

The constant of proportionality is 3.5 dollars per item.