To determine the correct equation that describes the relationship between the number of minutes Ray walks (let's represent this as \( x \)) and the number of calories he burns (let's represent this as \( y \)), we need to analyze the options provided based on the likely linearity and slope relationship shown in the graph.
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Option A: \( y = x - 4 \) - This suggests that as \( x \) increases, \( y \) increases but starts at -4 when \( x = 0 \). This doesn't appear to describe a typical walking scenario where calories burned starts at a reasonable non-negative value.
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Option B: \( y = 4x \) - This implies that for every minute walked, Ray burns 4 times that number in calories, which is a direct proportional relationship. It means as \( x \) increases, \( y \) also increases linearly.
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Option C: \( y = x + 4 \) - This suggests that starting from \( x = 0 \), Ray burns 4 calories in addition to the number of minutes walked. While this is a positive slope, it's less likely for calories burned to increase directly with minutes plus a constant 4.
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Option D: \( y = \frac{x}{4} \) - This indicates that for every 4 minutes walked, Ray burns 1 calorie. This would represent a much slower burn rate, which is typically not how calorie burning from walking is represented.
The most reasonable option that indicates a good calorie-burning rate associated with walking (assuming the slope is reasonable) would likely be:
B: \( y = 4x \)
This suggests that Ray burns 4 calories for each minute of walking, which sounds plausible.
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