Respuesta :

Edufirst

Answer:

  • The constant of proportionality is the value of the ratio of the two proportional quantities.

Explanation:

Two quantities are proportional or have a direct proportional relationship if their quotient, also called ratio, is constant.

In such a case you can write:

  • Amount of x / amount of y = constant, or simply:

  • [tex]\frac{x}{y}=k[/tex]

Where the notation x / y is the ratio and k is the constant of proportionality.

From that expresssion, it is proved that when two quantities are proportional, if one doubles the other also doubles, if one quadruples the other also quadruples, and in general, if one is multiplied by a factor the other is multiplied by the same factor;

For example, the number of pencils and the number of boxes of pencils are proportional because:

  • 12 pencils / 1 box = 12

  • 24 pencil / 2 box = 12

  • 48 pencil / 4 box = 12

  • 120 pencils / 10 boxes 12

The constant of proportionality is 12, indicating that each box contains 12 pencils; thus, both quantities (number of pencils and number of boxes of pencils) have a constant ratio of 12.

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