To determine whether the given relationship between the number of days (x) and cost (y) is proportional, we can analyze the values provided.
Part A: Is this a proportional relationship?
A relationship is considered proportional if the ratio of \( y \) to \( x \) (i.e., \( \frac{y}{x} \)) is the same for all pairs of values.
Let's calculate \( \frac{y}{x} \) for each pair:
- For (6, 2): \( \frac{2}{6} = \frac{1}{3} \)
- For (9, 3): \( \frac{3}{9} = \frac{1}{3} \)
- For (24, 8): \( \frac{8}{24} = \frac{1}{3} \)
- For (3, 1): \( \frac{1}{3} = \frac{1}{3} \)
Since the ratio \( \frac{y}{x} \) is constant ( \( \frac{1}{3} \) ) across all pairs, this is a proportional relationship.
Part B: If this is a proportional relationship, what is the constant?
The constant of proportionality can be determined from the consistent ratio we calculated.
Constant: \( \frac{1}{3} \)
Part C: If this is a proportional relationship, write a direct proportion equation.
The direct proportion equation can be expressed in the form \( y = kx \), where \( k \) is the constant of proportionality.
Using the constant we found:
Direct proportion equation: \( y = \frac{1}{3}x \)
In summary:
- Part A: Yes, it is a proportional relationship.
- Part B: \( \frac{1}{3} \)
- Part C: \( y = \frac{1}{3}x \)
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