Question

Whether x and y show direct variation, inverse variation, or neither. xy=1/4

(a) Direct Variation
(b) Inverse Variation
(c) Neither
(d) Not enough information

Explanation: The given equation xy = 1/4 can be rewritten as y = 1/(4x). This is in the form y = k/x, which is the equation for inverse variation. Therefore, the correct answer is:

Answer: (b) Inverse Variation

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Answer 1

The equation xy = 1/4 is an inverse variation with the form y = 1/(4x), which contrasts with direct variation where variables change together proportionally.

Step-by-step explanation:

The equation xy = 1/4 represents an inverse variation between the variables x and y. This can be seen as the equation is restructured in the form y = 1/(4x), matching the general format for inverse proportionality, y = k/x, where k remains constant as x and y vary inversely. In contrast to this, direct variation would be in the form y = kx, which depicts a situation where y increases as x increases, often represented graphically as a straight line through the origin (0, 0), indicating a linear relationship between the variables.