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Is this a proportional relationship? Explain your reasoning.

a) Yes, it is a proportional relationship because the ratio of distance to time is constant.
b) No, it is not a proportional relationship because the distance and time values do not form a straight line.
c) Yes, it is a proportional relationship because the distance and time values are equal.
d) No, it is not a proportional relationship because the equation is not linear.

User JeffO
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1 Answer

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Final answer:

The relationship is proportional because the given equation is linear with a y-intercept of 0, indicating a constant ratio between distance and time which results in a straight line when graphed.

Step-by-step explanation:

To determine whether there is a proportional relationship between two quantities, we should check if the ratio between them is constant. In this case, the given equation is y = (2.0 km/min) t, which can be seen as y = mt + b where m is the slope (rate of change) and b is the y-intercept. When b = 0, as in this equation, it means the line goes through the origin (0,0) on a graph. This indicates a directly proportional relationship because as time (t) increases, the distance (y) increases at a constant rate.

For the relationship to be proportional, there should be a straight line when plotted on a graph. As per the information given, the equation y = (2.0 km/min) t + 0 implies a linear graph with a slope of 2.0 km/min and a y-intercept of 0. This satisfies the condition for a proportional relationship where the equation is of the form y = kx, and there is no constant term added (b = 0). Therefore, statement a) 'Yes, it is a proportional relationship because the ratio of distance to time is constant' is the correct answer.

User Rafael Baptista
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