To determine if \(x\) (the distance in miles) and \(y\) (the amount charged in dollars) have a proportional relationship, we need to check if the ratios of \(y\) to \(x\) are constant across the given data points.
Let's calculate the ratio \( \frac{y}{x} \) for each data pair:
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For \(x = 22\), \(y = 48\): \[ \frac{y}{x} = \frac{48}{22} \approx 2.18 \]
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For \(x = 32\), \(y = 68\): \[ \frac{y}{x} = \frac{68}{32} = 2.125 \]
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For \(x = 38\), \(y = 80\): \[ \frac{y}{x} = \frac{80}{38} \approx 2.11 \]
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For \(x = 43\), \(y = 90\): \[ \frac{y}{x} = \frac{90}{43} \approx 2.09 \]
The ratios are not constant; they vary for each pair of values. Therefore, \(x\) and \(y\) do not have a proportional relationship.
The answer is: no.