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.

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

                      )

triangle abd and cba are similar,

                            (2)

triangle cad and cba are similar,

                      )

using (1), (2) and (3), we get

hence proved.

therefore option 2 is correct.