Given that x and y vary directly, write the equation relating x and y if x = 3 when y = 24.

First, write the general form for direct variation.

y = kx

Now plug in the x- and y-values to find k.

24 = k(3)

Solve for k.

k = 8

That means our equation is:

y = 8x

If y varies directly with x, and the constant of variation is k = ½ , find y when x = 30.

Write the general form for direct variation.

y = kx

Plug in the given value for k.

Finally, plug in 30 for x and solve for y.

y = 15

Given that x and y vary directly, and that y = 3000 when x = 250, find y when x = 300.

First, find the equation.

Write the general form for direct variation.

y = kx

Now plug in x- and y-values to find k.

3000 = k(250)

Solve for k:

k = 12

y = 12x

Now plug in x = 300 and solve for y:

y = 12(300)

y = 3600