Question

How do you write a direct variation equation that relates x and y if y = -8 when x = -2 then how do you find x when y = 32?

Answer 1

`x = 8` when `y = 32`

Explanation:

Given: `x` varies directly to `y`. If `y = -8` when `x = -2` find `x` when `y = 32`

Direct variation: `y = kx`, where `k` is the constant of proportionality

Find `k:" " -8 = k(-2)`

`k = (-8)/(-2) = 4`

`y = 4x`

Find `x` when `y = 32`:

`32 = 4x`

`x = 32/4 = 8`

CHECK using another method where you don't need to find `k`:

`y_1/y_2 = x_1/x_2`

`(-8)/(32) = (-2)/x_2`

Use the cross-product to find `x_2`, `x` when `y = 32`:

`-8 x_2 = -2(32)`

`-8x_2 = -64`

`x_2 = (-64)/(-8) = 8`