Assume that y varies inversely with x and that y is 2 when x is 4. Which of the following is the equation of inverse variation?

Question

4469 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-05-24T09:08:26

$y = \frac{8}{x}$ $y=8/x$

The question state: "Which of the following...." The is nothing shown after the question so ' the following ' part of the question is missing.

Given: $y α \frac{1}{x} The α means - proportional to$ $" "y" " alpha" " 1/x" The "alpha" means - proportional to"$

Let $k$ $k$ be the coefficient of proportionality

$y = k \times \frac{1}{x} = \frac{k}{x}$ $y=kxx 1/x = k/x$

Given that at $y = 2$ $y=2$ the value of $x$ $x$ is 4

$2 = \frac{k}{4}$ $2=k/4$

Multiply both sides by 4

$8 = k$ $8=k$

So the final equation is:

$y = \frac{8}{x}$ $y=8/x$