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 (kk), we use the formula for direct proportionality:

k=xyk = \frac{x}{y}

Let's calculate kk for each pair of xx and yy values from the table:

  1. For x=24x = 24 and y=6y = 6: k=246=4k = \frac{24}{6} = 4

  2. For x=28x = 28 and y=7y = 7: k=287=4k = \frac{28}{7} = 4

  3. For x=12x = 12 and y=3y = 3: k=123=4k = \frac{12}{3} = 4

  4. For x=16x = 16 and y=4y = 4: k=164=4k = \frac{16}{4} = 4

Since kk is consistent across all pairs, the constant of proportionality is:

k=4\boxed{k = 4}

Would you like me to provide further explanations or explore related concepts? Here are some follow-up questions to deepen your understanding:

  1. What happens if kk is not consistent across all pairs?
  2. How can we identify direct proportionality from a graph?
  3. What are real-world examples of direct proportionality?
  4. How does this concept differ from inverse proportionality?
  5. Can you calculate yy if kk and xx are known?

Tip: Always verify proportionality by checking that the ratio (kk) 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