Question

xy - 11= 5

y/x = 5
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fraction

Tell whether x and y show direct variation. Explain your reasoning.

Answer 1

An equation shows inverse variation if it can be represented in the form $y = \frac{k}{x}$. The first equation can be rearranged into this form:

$xy - 11 = 5$
$xy = 16$
$y = \frac{16}{x}$

This is in the form $y = \frac{k}{x}$, so the first equation shows inverse variation.

An equation shows direct variation if it can be represented in the form $y = kx$. The second equation can be rearranged into this form:

$\frac{y}{x} = 5$
$y = 5x$

This is in the form $y = kx$, so the second equation shows direct variation.