Which table represents a direct variation? table a table b table c table d

The table that represents a direct variation is:

                               Table B.

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

Now in Table A:

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

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:

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:

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:

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.

see attached

step-by-step explanation:

given the function as;

write the equation replacing f(x) with y

form   and fill a table containing values of y with corresponding values of x

you can take a range for   values of x as -3≤x≤3

solving for x=-3

for x=-2

repeat the same procedure to get the values of y for the remaining ,x=-1 to x=3

plot the values of y against values   of x and obtain the following graph