Question

which equation represents an inverse variation?
$\frac{y}{x} = 40$
$x = \frac{y}{40}$
$y = 40x$
$y = \frac{40}{x}$

Explanation:

Step1: Recall inverse variation form

Inverse variation follows $xy = k$ or $y=\frac{k}{x}$, where $k$ is a non-zero constant.

Step2: Analyze each option

• Option 1: $\frac{y}{x}=40$ rearranges to $y=40x$ (direct variation).
• Option 2: $x=\frac{y}{40}$ rearranges to $y=40x$ (direct variation).
• Option3: $y=40x$ is direct variation.
• Option4: $y=\frac{40}{x}$ matches $y=\frac{k}{x}$ with $k=40$.

Answer:

D. $y = 40/x$