Determine whether y varies directly with x. if so, find the constant of variation and write the equation. x | y -2 | -4 -4 | -8 -16 | -32 a. no b. yes; k=-2 and y=-2x c. yes; k=1/2 and y=1/2x d. yes; k=2 and y=2x

The correct option is d.

Step-by-step explanation:

If y varies directly with x, then y is directly proportional to x.

             .... (1)

Where, k is constant of variation.

From the given table it is clear that the value of y is -4 at x=-2.

Put x=-2 and y=-4 in equation (1).

Divide both sides by -2.

The value of k is 2. Put this value in equation (1), to find the relation between x and y.

At x=-4,

At x=-16,

All the points of the table satisfy the equation. It means y is directly proportional to x, the constant of variation is 2 and required equation is y=2x.

Hence option d is correct.

step-by-stp

the correct answer is the section c