Chapter 8.6, Problem 30E

To determine

To write:

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

Answer to Problem 30E

Our requireddirect variation equation would be $y=-\frac{4}{3}x$ .

Explanation of Solution

Given:

An ordered pair: $(12,-16)$

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:

  $\begin{array}{l}y=kx\left(\text{General equation of direct variation}\right)\\ -16=k(12)\left(\text{Substituting }x=12\text{and }y=-16\right)\\ -16=12k\\ 12k=-16\left(\text{Switching sides}\right)\\ \frac{12k}{12}=\frac{-16}{12}\left(\text{Dividing both sides by }12\right)\\ k=-\frac{4}{3}\end{array}$

Upon substituting $k=-\frac{4}{3}$ in general direct variation equation, we will get:

  $y=-\frac{4}{3}x$

Therefore, the required direct variation equation would be $y=-\frac{4}{3}x$ .