Question

Suppose y varies directly with x. If y = –4 when x = 8, what is the equation of direct variation? Complete the steps to write the equation of direct variation.

Answer 1

Direct variation is of the form y=kx. We are given the point (8, -4) so we can solve for k, the constant of variation...

-4=8k, divide both sides by 8

-4/8=k

k=-0.5, so our equation is:

y=-0.5x,

Answer 2

The equation of direct variation is
`y=-(1)/(2)x`.

Explanation:

If y varies directly with x, then

`y\propto x`

`y=kx` ..... (1)

Where, k is constant of proportionality.

It is given that the value of y is -4 at x=8.

Substitute x=8 and y=-4 in the above equation.

`-4=k* 8`

Divide both sides by 8.

`(-4)/(8)=k`

`-(1)/(2)=k`

The value of k is -1/2.

Substitute
`k=-(1)/(2)` in equation (1).

`y=-(1)/(2)x`

Therefore the equation of direct variation is
`y=-(1)/(2)x`.