# For the direct variation y = (3/4) when x = (1/8), how do you find the constant of variation and find the value of y when x = 3?

Jan 21, 2017

For direct variation $y = \frac{3}{4}$ when $x = \frac{1}{8}$ the constant of variation is $k = 6$, and when $x = 3$ we have $y = 18$.

#### Explanation:

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

The statement y is proportional to x, is the same as y equals x times a constant k.

$y \propto x \iff y = k x$

Then we can plug in the case we already know if $y = \frac{3}{4}$ then $x = \frac{1}{8}$.

$\implies \frac{3}{4} = k \frac{1}{8}$ So we need to solve for k

$\iff 8 \left(\frac{3}{4}\right) = \frac{24}{4} = 6 = k$ Multiply both sides by 8 and simplify

So, $k = 6$

Then we have $y = 6 x$

so we plug in $x = 3$

$y = 6 \left(3\right) = 18$