Question

Which table represents a direct variation? Table A Table B Table C Table D

Answer 1

Table B as only in B :
$\frac{y}{x } = 3$
for every y and x values

Answer 2

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:

        $\dfrac{y}{x}=k$

Now in Table A:

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

• $\dfrac{7}{4}$

• $\dfrac{9}{6}=\dfrac{3}{2}$

• $\dfrac{11}{8}$

• $\dfrac{13}{10}$

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:

• $\dfrac{12}{4}=3$

• $\dfrac{18}{6}=3$

• $\dfrac{24}{8}=3$

• $\dfrac{30}{10}=3$

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:

• $\dfrac{1}{4}$

• $\dfrac{3}{6}=\dfrac{1}{2}$

• $\dfrac{5}{8}$

• $\dfrac{7}{10}$

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:

• $\dfrac{3}{4}$

• $\dfrac{3}{6}=\dfrac{1}{2}$

• $\dfrac{3}{8}$

• $\dfrac{3}{10}$

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.