Question

which equation represents an inverse variation?
$y/x = 40$
$x = y/40$
$y = 40x$
$y = 40/x$

Explanation:

Step1: Recall inverse variation form

An inverse variation follows the form $y = \frac{k}{x}$ (or $xy=k$, where $k$ is a non-zero constant).

Step2: Analyze each option

• Option 1 ($\frac{y}{x}=40$): Rearranges to $y=40x$, which is direct variation.
• Option 2 ($x=\frac{y}{40}$): Rearranges to $y=40x$, which is direct variation.
• Option 3 ($y=40x$): This is direct variation, not inverse.
• Option 4 ($y=\frac{40}{x}$): Matches the inverse variation form $y=\frac{k}{x}$ with $k=40$.

Answer:

$y = \frac{40}{x}$