The problem asks for the constant of proportionality based on the data provided in the table. Here's the information in the table:

• Number of Items (x): 2, 4, 6, 8
• Cost ($) (y): 14, 28, 42, 56

The constant of proportionality (k) in a direct variation is calculated using the formula:

$k = \frac{y}{x}$

Let's calculate $k$ for each pair of $x$ and $y$:

1. When $x = 2$ and $y = 14$: $k = \frac{14}{2} = 7$

2. When $x = 4$ and $y = 28$: $k = \frac{28}{4} = 7$

3. When $x = 6$ and $y = 42$: $k = \frac{42}{6} = 7$

4. When $x = 8$ and $y = 56$: $k = \frac{56}{8} = 7$

Since the constant of proportionality is consistent across all pairs, the constant of proportionality $k$ is 7.

Would you like more details on this, or do you have any questions?

Here are 5 related questions you might consider:

1. How would the constant of proportionality change if the cost were to double?
2. What does the constant of proportionality represent in this context?
3. Can you determine the cost if the number of items was 10?
4. How do you identify direct proportionality from a table of values?
5. What would the table look like if the relationship was inversely proportional?

Tip: To check if a relationship is directly proportional, divide the values of $y$ by $x$ for different pairs. If the result (k) is the same for all pairs, the relationship is directly proportional.