Question

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

Answer 1

yes.
the every x value multiplying 2 gets the corresponding y values, so y=2x
d is the correct answer.

Answer 2

The correct option is d.

Explanation:

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

`y\propto x`

`y=kx` .... (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).

`-4=k(-2)`

Divide both sides by -2.

`2=k`

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

`y=2x`

At x=-4,

`y=2(-4)=-8`

At x=-16,

`y=2(-16)=-32`

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.