Chapter 11, Problem 27CR

To determine

Write an equation of the inverse variation that includes $y=7\text{when}x=3$

Answer to Problem 27CR

The required equation: $y=\frac{21}{x}$

Explanation of Solution

Given: Write an equation of the inverse variation that includes $y=7\text{when}x=3$

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.

Calculation:

The equation for inverse proportion: $y=\frac{k}{x}\text{or}y·x=k$  is constant

The point: $(3,7)\text{or}y=7\text{when}x=3$

  $\Rightarrow y·x=(7·3)=21$

The Required equation: $y=\frac{21}{x}$

Thus, the required equation:

  $y=\frac{21}{x}$