Chapter 8.6, Problem 29E

To determine

To write:

A direct variation equation that has the given ordered pair as a solution.

Answer to Problem 29E

Our requireddirect variation equation would be $y=\frac{1}{2}x$ .

Explanation of Solution

Given:

An ordered pair: $(-8,-4)$

Concept used:

We know that y varies directly with x , if $y=kx$ , where k represents constant of proportionality.

Calculation:

To write our required direct variation equation, we will substitute coordinates of given ordered pair in general equation of direct variation and solve for k as shown below:

  $\begin{array}{l}y=kx\left(\text{General equation of direct variation}\right)\\ -4=k(-8)\left(\text{Substituting }x=-8\text{and }y=-4\right)\\ -4=-8k\\ -8k=-4\left(\text{Switching sides}\right)\\ \frac{-8k}{-8}=\frac{-4}{-8}\left(\text{Dividing both sides by }-8\right)\\ k=\frac{1}{2}\end{array}$

Upon substituting $k=\frac{1}{2}$ in general direct variation equation, we will get:

  $y=\frac{1}{2}x$

Therefore, the required direct variation equation would be $y=\frac{1}{2}x$ .