### Video Transcript

π¦ varies inversely with π₯ cubed. The constant of proportionality is equal to six. Which of the following equations represents this relation? Is it a) π¦ equals six divided by π₯ cubed, b) π¦ equals six divided by π₯, c) π¦ equals six minus π₯ cubed, or d) π¦ equals six π₯ cubed?

As π¦ varies inversely with π₯ cubed, we can say that π¦ is proportional to one divided by π₯ cubed or π¦ is proportional to one over π₯ cubed. Replacing our proportion symbol with a constant of proportionality gives us the equation π¦ equals π divided by π₯ cubed.

As the constant of proportionality in this question is equal to six, we can write π¦ equals six divided by π₯ cubed. Therefore, the correct answer in this case is a: π¦ equals six divided by π₯ cubed.

As an aside, answer b π¦ equals six divided by π₯ would be the answer if π¦ was varying inversely with π₯. In the same way answer d π¦ equals six π₯ cubed would be the answer if π¦ was varying directly with π₯ cubed. Answer c does not demonstrate a direct or an inverse proportion between π₯ and π¦.