Video: Writing Proportion Equations Involving Inverse Variation

𝑦 varies inversely with π‘₯Β³. The constant of proportionality is 6. Which of the following equations represents this relation? [A] 𝑦 = 6/π‘₯Β³ [B] 𝑦 = 6/π‘₯ [C] 𝑦 = 6 βˆ’ π‘₯Β³ [D] 𝑦 = 6π‘₯Β³?

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Video Transcript

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

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

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

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

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