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Reasoning  The equation below describes a proportional relationship between x and y. What is the constant of​ proportionality? Use pencil and paper. Explain why your answer is called the​ "constant of​ proportionality."

yequals5.13x
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Part 1
The constant of proportionality is
  
enter your response here.

1 answer

In the equation \( y = 5.13x \), the constant of proportionality is the coefficient of \( x \), which is 5.13. This means that for every unit increase in \( x \), \( y \) increases by 5.13 units.

Explanation:

The term "constant of proportionality" refers to the constant factor that relates two quantities in a proportional relationship. In other words, it shows how much one quantity will change when the other quantity changes.

In this equation:

  • \( y \) is directly proportional to \( x \).
  • The equation tells us that \( y \) is equal to 5.13 times \( x \).
  • Therefore, 5.13 is the rate at which \( y \) changes with respect to changes in \( x \), hence it is the constant of proportionality.

So the answer is: Constant of proportionality: 5.13.