To determine which statement is true regarding the line that passes through given coordinates and whether it represents a proportional relationship, we must first understand the concept of a proportional relationship.
A proportional relationship between two quantities means that their ratio is constant, or equivalently, that the line graph of the relationship is a straight line that passes through the origin (0,0).
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If the line passes through the origin (0,0), this indicates that there is a proportional relationship because when one variable is zero, so is the other.
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If the line does not pass through the origin, then it indicates that there is no proportional relationship. The y-intercept of the line is not zero, which means that the ratio is not constant when one of the variables is zero.
Based on this understanding, we can analyze the provided options:
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A. The line that passes through the given coordinates represents a proportional relationship because the line does not pass through the origin. (False)
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B. The line that passes through the given coordinates represents a proportional relationship because the line passes through the origin. (True, if it does pass through the origin)
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C. The line that passes through the given coordinates does not represent a proportional relationship because the line passes through the origin. (False)
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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. (True, if it does not pass through the origin)
To conclude, you would need to check whether the coordinates provided (not visible in your prompt) indicate a line that passes through the origin or not. If the line through those coordinates passes through the origin, then B is true. If it does not, then D would be true.
Please provide the coordinates if you need a specific answer based on those values.
1 answer