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Inverse Variation - Concept
When modeling real world situations, we often use what's called inverse variation to describe a relation between two variables. Inverse variation is a relation in which the absolute value of one variable gets smaller while the other gets larger. Inverse variation and direct variation are important concepts to understand when learning equations and interpreting graphs.
Inverse relationships are really important not only in Math but especially when you guys get into Physics. So this is a concept you're going to want to keep tacked in the back of your brain for when you start studying Physics.
Inverse Variation is described by the equation y=k divided by x where k is called the constant of variation. I don't know about you guys but I personally don't like fractions that much so this makes me a little nervous. So instead of working with fractions a lot of people choose to rewrite the same equation by solving for k. If you multiply both sides of this this equation by x you'll get k is equal to the product of y and x. For me personally that's a lot easier to wrap my head around.
Another thing that has to do with this property is what was called the product rule of for inverses variation. It tells us that if x1 y1 and x2 y2 are solutions to an inverse variation relation then x1 times y1 is equal to x2 times y2. That's just reiterating that any time you have inverse variation the product of the x and y solution pair will be equal to the product of another x and y solution pair like this. You always get the same number called k when you multiply them together.
One last thing I want to leave you with with inverse variation is that as one variable gets bigger the other variables are going to get smaller that's kind of like what inverse means right, if they vary inversely as one gets larger the other one is going to get smaller. And that's going to become really important in your future math classes when you start to looking at graphs of these kinds of relationships. So again before you start doing your homework my one like most important tip that I hope you guys remember is that if you don't like working with fractions that's totally fine you don't have to, rewrite that equation as this and looked for two numbers the x and y pairs when you find their product it's going to be equal to the same number over and over and over again.