Chapter 5.2, Problem 1P

Determine whether each equation represents a direct variation. If it does, find the constant of variation.

$-8y=2x$

To determine

To find: The constant of variation for the equation $-8y=2x$

Answer to Problem 1P

Yes, the equation $-8y=2x$ represents a direct variation with the constant of variation is $k=-\frac{1}{4}$

Explanation of Solution

Given information:

The equation is $-8y=2x$ .

The given equation can be rewritten as

  $\begin{array}{l}-8y=2x\\ \Rightarrow y=-\frac{2}{8}x\\ \Rightarrow y=-\frac{1}{4}x\end{array}$

Conclusion:

It is observed that the equation $y=-\frac{1}{4}x$ is in the form of $y=kx$ . Therefore, the equation represents a direct variation with the constant of variation is $k=-\frac{1}{4}$ .