Which statement best defines Inverse Variation?

Which statement best defines Inverse Variation?

• A. A constant sum relationship between variables
• B. A linear relationship with a nonzero intercept
• C. A relationship in which both variables increase together
• D. A situation in which one quantity increases while another quantity decreases

Answer: (D)

Inverse variation is the relationship where one quantity grows while another shrinks in such a way that their product stays the same. In mathematical terms, x and y satisfy xy = k, a constant, which makes y = k/x. That means as one variable increases, the other decreases, directly capturing the idea that one quantity goes up while the other goes down. The statement describing this behavior is the best fit because it reflects the defining feature: a rise in one variable forces a fall in the other to keep the product constant. The other descriptions point to different types of relationships—constant sum describes a straight-line relation y = c − x; a linear relation with a nonzero intercept is still a line; and both variables increasing together describes direct variation, not inverse.

Inverse variation is the relationship where one quantity grows while another shrinks in such a way that their product stays the same. In mathematical terms, x and y satisfy xy = k, a constant, which makes y = k/x. That means as one variable increases, the other decreases, directly capturing the idea that one quantity goes up while the other goes down.

The statement describing this behavior is the best fit because it reflects the defining feature: a rise in one variable forces a fall in the other to keep the product constant. The other descriptions point to different types of relationships—constant sum describes a straight-line relation y = c − x; a linear relation with a nonzero intercept is still a line; and both variables increasing together describes direct variation, not inverse.