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

Answer:

The equation of direct variation is $y=-\frac{1}{2}x$.

Step-by-step 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.

$-4=k\times 8$

Divide both sides by 8.

$\frac{-4}{8}=k$

$-\frac{1}{2}=k$

The value of k is -1/2.

Substitute $k=-\frac{1}{2}$ in equation (1).

$y=-\frac{1}{2}x$

Therefore the equation of direct variation is $y=-\frac{1}{2}x$.