Chapter 5.2, Problem 8LC

To determine

To show:that $p$ varies directly with $q$ .

Answer to Problem 8LC

The given statement is always true.

The variable $p$ also varies directly with $q$ .

Explanation of Solution

Given information:

The system information is: $q$ varies directly with $p$ , does this imply $p$ also varies directly with $q$ .

Calculation:

An equation is called a direct variation if it is in theform of $y=kx,$ where, $k\ne 0$ is the constant of variation.

The value of the constant of variation is obtained by dividing $x$ :

  $k=\frac{y}{x}$

If $q$ varies directly with $p,$ then the equation of the direct variation is

  $q=kp$

From the above equation, isolate the variable $p:$

  $p=\frac{1}{k}q$ .

  $rk$ .

Thus, the variable $p$ also varies directly with $q$ .

Therefore, the given statement is always true.