Video: Finding the Constant of Proportionality

𝑦 varies inversely with π‘₯. Given that 𝑦 = 8 when π‘₯ = 7, what is the constant of proportionality?

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Video Transcript

𝑦 varies inversely with π‘₯. Given that 𝑦 equals eight when π‘₯ equals seven, what is the constant of proportionality?

Remember that when 𝑦 varies inversely with π‘₯, it’s in the form 𝑦 equals π‘˜ over π‘₯, where π‘˜ is the constant of proportionality. We can use this function and plug in what we know to solve for π‘˜.

We know that when π‘₯ is seven, 𝑦 equals eight. To get π‘˜ by itself, we’ll multiply by seven over one on both sides. On the right side, divided by seven multiplied by seven over one cancels each other out, leaving us with π‘˜. On the left hand side, we multiply seven by eight to get 56.

Our final answer the constant of proportionality equals 56.

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