Final answer:
The equations y = 1.95x, y = 2x, and y = 0.5x (Options A, C, and D) represent directly proportional relationships, as they are in the form y = kx where k is the constant of proportionality.
Step-by-step explanation:
To determine which equation represents a proportional relationship, we need to identify the equation that is of the form y = kx, where k is the constant of proportionality and the graph of the equation would pass through the origin (0, 0). A proportional relationship is one where the ratio between the two variables is constant. Therefore, additional terms (like a constant being added or subtracted) would disqualify an equation from representing a directly proportional relationship.
Looking at the provided options:
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- Option A: y = 1.95x is in the form y = kx and suggests a proportional relationship where k is 1.95.
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- Option B: y = x - 1.95 includes a subtraction of 1.95, which means it is not purely proportional.
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- Option C: y = 2x is also in the form y = kx, indicating another proportional relationship with k as 2.
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- Option D: y = 0.5x is equally valid for a proportional relationship with k being 0.5.
The context of the original problem would further dictate which specific equation is correct if additional information was provided about the rate of change. However, based on the information at hand, options A, C, and D all represent proportional relationships.