To analyze a proportional relationship using ordered pairs, we first need those ordered pairs. A proportional relationship can be expressed in the form \( y = kx \), where \( k \) is the constant of proportionality.
To find the constant of proportionality \( k \):
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Identify the Ordered Pairs: Let's say you have ordered pairs like \( (x_1, y_1), (x_2, y_2), (x_3, y_3), \) etc.
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Calculate \( k \) for Each Pair: You can calculate \( k \) using \( k = \frac{y}{x} \) for each pair:
- From the first pair: \( k_1 = \frac{y_1}{x_1} \)
- From the second pair: \( k_2 = \frac{y_2}{x_2} \)
- From the third pair: \( k_3 = \frac{y_3}{x_3} \)
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Check Consistency: If all \( k \) values are equal (i.e., \( k_1 = k_2 = k_3 = k \)), then it confirms that the relationship is proportional, and you can denote that constant as the constant of proportionality.
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Example: Suppose you have the pairs (2, 4), (3, 6), and (4, 8):
- For (2, 4): \( k = \frac{4}{2} = 2 \)
- For (3, 6): \( k = \frac{6}{3} = 2 \)
- For (4, 8): \( k = \frac{8}{4} = 2 \)
- Since all values of \( k \) are equal and equal to 2, the constant of proportionality is \( k = 2 \).
If you provide the specific ordered pairs, I can help you find the constant of proportionality for those values!