Math Problem Statement
Calculate the constant of proportionality (k) for the relationship given the table of x and y values.
Solution
To calculate the constant of proportionality (), we use the formula for direct proportionality:
Let's calculate for each pair of and values from the table:
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For and :
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For and :
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For and :
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For and :
Since is consistent across all pairs, the constant of proportionality is:
Would you like me to provide further explanations or explore related concepts? Here are some follow-up questions to deepen your understanding:
- What happens if is not consistent across all pairs?
- How can we identify direct proportionality from a graph?
- What are real-world examples of direct proportionality?
- How does this concept differ from inverse proportionality?
- Can you calculate if and are known?
Tip: Always verify proportionality by checking that the ratio () remains constant across all pairs!
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Math Problem Analysis
Mathematical Concepts
Direct Proportionality
Ratios
Formulas
k = x / y
Theorems
Constant Ratio Theorem
Suitable Grade Level
Grades 6-8