To determine if \( x \) (the length of hallway in feet) and \( y \) (the number of tiles) have a proportional relationship, we need to check if the ratio \( \frac{y}{x} \) is constant for all the given pairs of values.
Let's calculate the ratio \( \frac{y}{x} \) for each pair:
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For \( x = 2.5 \) and \( y = 30 \): \[ \frac{y}{x} = \frac{30}{2.5} = 12 \]
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For \( x = 3.5 \) and \( y = 42 \): \[ \frac{y}{x} = \frac{42}{3.5} = 12 \]
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For \( x = 6 \) and \( y = 72 \): \[ \frac{y}{x} = \frac{72}{6} = 12 \]
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For \( x = 7 \) and \( y = 84 \): \[ \frac{y}{x} = \frac{84}{7} = 12 \]
Since the ratio \( \frac{y}{x} \) is the same (12) for all the pairs, \( x \) and \( y \) do have a proportional relationship.
Answer: yes