To determine which statement is true, let’s first clarify the concept of a proportional relationship. A relationship is considered proportional if it can be represented by a line that passes through the origin (0, 0), indicating that when one variable is zero, the other variable is also zero.
Now, let's analyze the statements provided:
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A. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin.
- This is incorrect. If the line passes through the origin, it may represent a proportional relationship.
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B. The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin.
- This statement is true if the line indeed passes through the origin and the relationship is linear.
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C. The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin.
- This is incorrect, as a line that does not pass through the origin is typically indicative of a non-proportional relationship.
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D. The line that passes through the given coordinates does not represent a proportional relationship because the line does not pass through the origin.
- This is also true if the line does not pass through the origin, as it implies a non-proportional relationship.
Therefore, the true statements depend on whether the line passes through the origin or not.
If the line passes through the origin, then the correct answer is B. If the line does not pass through the origin, then the correct answer is D.
Without the specific coordinates to graph, we can't determine which one is definitively true but can explain the conditions under which each could be true.