To determine which table shows a proportional relationship between \( x \) and \( y \), we need to check if \( y/x \) remains constant for all values of \( x \) and \( y \).
Let's check each response:
-
For the first table:
- \( \frac{y}{x} \) values:
- \( \frac{8}{40} = 0.2 \)
- \( \frac{10}{50} = 0.2 \)
- \( \frac{14}{60} \approx 0.2333 \)
- \( \frac{18}{90} = 0.2 \)
- Since the fractions are not all the same, this table does not show a proportional relationship.
- \( \frac{y}{x} \) values:
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For the second table:
- \( \frac{y}{x} \) values:
- \( \frac{2}{4} = 0.5 \)
- \( \frac{3.5}{7} = 0.5 \)
- \( \frac{4}{8} = 0.5 \)
- \( \frac{5}{10} = 0.5 \)
- All values are the same (0.5), so this table does show a proportional relationship.
- \( \frac{y}{x} \) values:
-
For the third table:
- \( \frac{y}{x} \) values:
- \( \frac{6}{1} = 6 \)
- \( \frac{8}{2} = 4 \)
- \( \frac{10}{3} \approx 3.33 \)
- \( \frac{12}{4} = 3 \)
- The values are not the same, so this table does not show a proportional relationship.
- \( \frac{y}{x} \) values:
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For the fourth table:
- \( \frac{y}{x} \) values:
- \( \frac{6}{2} = 3 \)
- \( \frac{10}{4} = 2.5 \)
- \( \frac{21}{7} = 3 \)
- \( \frac{24}{8} = 3 \)
- The fractions are not the same; thus, this table does not show a proportional relationship.
- \( \frac{y}{x} \) values:
Therefore, the second table shows a proportional relationship between \( x \) and ( y .
Answer: \( x \) 4 7 8 10; \( y \) 2 3.5 4 5 (shows a proportional relationship)
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