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Inverse Variation - Problem 2
An inverse variation is one that can be written as xy=k, where the product of each x and y pair is equal to the same constant. When given a relationship, solve the equation for "xy", meaning have xy on one side of the equal sign and the numbers on the other. This will allow you to see if the product of x and y is equal to some constant. If it is, then the relationship represents an inverse variation.
Here's a different type of problem you can see when you are working with inverse variation. We are given an equation of relationship and we are asked to tell whether or not it represents an inverse variation.
Well I know it would be an inverse variation if I get something like xy equals k, the product of x and y is equal to some constant some k number. So let's see if we can solve this equation for xy.
This is tricky for algebra students because usually you are solving for one letter at a time. Here I'm solving for the chunk like the product of x and y. So here it is right there good I'm lucky they're already grouped together. I want to get x and y all by itself right now it's been multiplied by 3. So let's go ahead and divide both sides by 3 and I'll have xy is equal to -10/3.
All right what that tells me is that because the product of x and y is equal to some constant, even though it's a fraction it's still just a regular old number, that tells me that yes this relation is inverse variation. X and y do change or vary in an inverse relationship style.
One thing I want to make sure you guys keep in the bracket back of your head when you are working with the inverse variation, is thinking about the domain. Domain means the x values or numbers that can be inputted. Think about if I were to put 0 here, I wouldn't be able to have a constant that is the same for every xy pair. Your domain values cannot include 0 ever for inverse variation because then your constant value wouldn't be the same for every product of x and y.
If that makes sense to you, you're like an A+ student you are on your way if that doesn't quite make sense yet don't be too hard on yourself because you're just starting with inverse variation but do keep in the back if your brain that for inverse variation the domain or x values cannot contain 0.