Bot GPT 4-o mini To determine if \( x \) (time in hours) and \( y \) (distance in miles) have a proportional relationship, we need to see if the ratio \( \frac{y}{x} \) is constant.
Let's calculate the ratio for each pair of values:
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For \( x = 1 \), \( y = 14 \): \[ \frac{y}{x} = \frac{14}{1} = 14 \]
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For \( x = 2 \), \( y = 28 \): \[ \frac{y}{x} = \frac{28}{2} = 14 \]
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For \( x = 3 \), \( y = 42 \): \[ \frac{y}{x} = \frac{42}{3} = 14 \]
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For \( x = 5 \), \( y = 70 \): \[ \frac{y}{x} = \frac{70}{5} = 14 \]
Since all the calculated ratios are equal, \( \frac{y}{x} = 14 \), we can conclude that there is a proportional relationship between \( x \) and \( y \).
Thus, the answer is yes, \( x \) and \( y \) have a proportional relationship.
The constant of proportionality is 14.
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