Given that 𝑦 varies inversely as 𝑥 squared, write an equation for 𝑦 in terms of 𝑥 using 𝑘 as a nonzero constant.
What do we know about inverse variation? Inverse variation is a relationship between two variables, where the product of the two variables is a constant. Given that 𝑦 varies inversely with 𝑥 squared, for us that means 𝑦 multiplied by 𝑥 squared equals a constant 𝑘.
But we need to rewrite this equation so that it says 𝑦 equals something. We want to know the relationship of 𝑦 in terms of 𝑥. And to do that, we’ll divide both sides of the equation by 𝑥 squared. On the left, it cancels out leaving us with 𝑦. And on the right, we see that the constant 𝑘 divided by 𝑥 squared should equal 𝑦.
𝑦 equals 𝑘 over 𝑥 squared.