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Which equation shows inverse variation? $\newline$ Choices: $\newline$ $(\frac{x}{36}) = y$ $\newline$ $yx = -74$

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Identify direct variation and inverse variation

Full solution

Q. Which equation shows inverse variation?

\newline

Choices:

\newline

(\frac{x}{36}) = y

\newline

yx = -74

Identify inverse variation: Identify the general form of inverse variation. $\newline$ Inverse variation is characterized by one variable being directly proportional to the reciprocal of another variable. The general form of inverse variation is $y = \frac{k}{x}$ , where $k$ is a constant.
Analyze first equation: Analyze the first equation $\frac{x}{36} = y$ . We need to determine if this equation can be expressed in the form $y = \frac{k}{x}$ . Rewriting the equation, we get $y = \frac{x}{36}$ . This equation suggests that $y$ is directly proportional to $x$ , not inversely proportional, as $y$ increases with an increase in $x$ .
Analyze second equation: Analyze the second equation $yx = -74$ . $\newline$ We need to determine if this equation can be expressed in the form $y = \frac{k}{x}$ . By isolating $y$ , we rewrite the equation as $y = \frac{-74}{x}$ . This equation fits the form $y = \frac{k}{x}$ with $k = -74$ , indicating that $y$ is inversely proportional to $x$ .
Determine inverse variation equation: Determine which equation shows inverse variation. $\newline$ Based on the analysis in the previous steps, the equation $yx = -74$ can be expressed in the form $y = \frac{k}{x}$ and therefore shows inverse variation.

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