To determine the correct responses, we need to understand the context provided by the table of (x, y) coordinates, which isn't fully visible in your question. However, I can guide you through the concepts of proportional relationships and help deduce the correct answers.
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Completing the Table: To choose which value completes the table from options A (1010), B (1111), C (1212), and D (1313), you would typically look for a pattern or rule that governs the x and y values. For instance, if the table suggests a linear equation or a specific relationship (like doubling, adding a constant, etc.), you'd match the response based on that rule.
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Proportional Relationships: A set of (x, y) coordinates represents two quantities that are proportional if:
- They can be expressed in the form \(y = kx\), where \(k\) is a constant.
- When graphed, the points lie on a straight line that passes through the origin (0, 0).
Given the response options, you can determine the correct answer to whether the points represent a proportional relationship based on where the line passes:
- B (Yes, the plotted points lie on a line that passes through the origin) indicates a proportional relationship.
- C (No, the plotted points lie on a line that does not pass through the origin) indicates a non-proportional relationship.
To conclude:
- Identify the value that fits in the table based on any visible pattern.
- Graph the coordinates (if possible) to visually confirm if they pass through the origin or not.
If you can provide the actual values associated with the (x, y) pairs in the table, I could help you deduce the answer more accurately.