Respuesta :

Table B as only in B :
[tex] \frac{y}{x } = 3 [/tex]
for every y and x values

Answer:

The table that represents a direct variation is:

                               Table B.

Step-by-step explanation:

We know that a table is of direct variation if for each x and y there exist a constant k such that:

        [tex]\dfrac{y}{x}=k[/tex]

Now in Table A:

We calculate the ratio of each y and x values as follows:

  • [tex]\dfrac{7}{4}[/tex]
  • [tex]\dfrac{9}{6}=\dfrac{3}{2}[/tex]
  • [tex]\dfrac{11}{8}[/tex]
  • [tex]\dfrac{13}{10}[/tex]

As we see that we did  not get a constant k from each of the ratios.

Hence, Table A is not a table of direct variation.

Table B:

We calculate the ratio of each y and x values as follows:

  • [tex]\dfrac{12}{4}=3[/tex]
  • [tex]\dfrac{18}{6}=3[/tex]
  • [tex]\dfrac{24}{8}=3[/tex]
  • [tex]\dfrac{30}{10}=3[/tex]

As we see that we get a constant k from each of the ratios.

Hence, Table B is  a table of direct variation.

Table C:

We calculate the ratio of each y and x values as follows:

  • [tex]\dfrac{1}{4}[/tex]
  • [tex]\dfrac{3}{6}=\dfrac{1}{2}[/tex]
  • [tex]\dfrac{5}{8}[/tex]
  • [tex]\dfrac{7}{10}[/tex]

As we see that we did  not get a constant k from each of the ratios.

Hence, Table C is not a table of direct variation.

Table D:

We calculate the ratio of each y and x values as follows:

  • [tex]\dfrac{3}{4}[/tex]
  • [tex]\dfrac{3}{6}=\dfrac{1}{2}[/tex]
  • [tex]\dfrac{3}{8}[/tex]
  • [tex]\dfrac{3}{10}[/tex]

As we see that we did  not get a constant k from each of the ratios.

Hence, Table D is not a table of direct variation.

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