Chapter 11, Problem 23GR

To determine

Find the condition of the inverse variation.

Answer to Problem 23GR

Explanation of Solution

Given:

Inverting a cup or glass means changing its orientation to the opposite direction. If positive values x and y are related by an inverse variation, do you think they increase and decrease together? Or do they move in opposite directions, one decreasing as the other increases?

Concept Used:

Inverse Variation The statement " y  varies inversely as  x  means that when  x  increases,  y decreases by the same factor.  In other words, the expression  $y=\frac{k}{x}\text{or}y·x=k$  is constant.

For inverse variation, use the equation $y=\frac{k}{x}$ , k as the constant of proportionality.

The expression  $y=\frac{k}{x}\text{or}y·x=k$  is constant.

If x and y both are positive, then one will increase and other will definitely decrease, because for inverse variation their product is always constant.

If for x and y , one is positive and other is negative , then according to the number line they move in opposite directions, one decreasing as the other increases but their product should always be constant.