𝑦 varies inversely with 𝑥. Given that 𝑦 equals eight when 𝑥 equals seven, what is the constant of proportionality?
Remember that when 𝑦 varies inversely with 𝑥, it’s in the form 𝑦 equals 𝑘 over 𝑥, where 𝑘 is the constant of proportionality. We can use this function and plug in what we know to solve for 𝑘.
We know that when 𝑥 is seven, 𝑦 equals eight. To get 𝑘 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 𝑘. On the left hand side, we multiply seven by eight to get 56.
Our final answer the constant of proportionality equals 56.