Inverse Variation Problem Solving

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So the bigger the value of x, the smaller the value of y will be.

That's inverse variation: as one goes up, the other goes down.

This is also called direct proportion: they're the same thing.

An example of this is relationship between age and height.

But that's not so terrible: the variation is defined in terms of a squared, so we'll just put in a squared for y.

We could also plug it in for x; it doesn't matter, as long as you're consistent.It looks pretty impenetrable at first, but don't panic.Pull out your equations, and start plugging things in.This might seem really complicated and confusing, but just remember the two formulas: y = kx for direct variation, and y = k/x for inverse variation.As you practice with example problems, you'll learn how to apply them to specific problems.As the age in years of a child increases, the height will also increase.In the abstract, we can express direct variation by using the equation y = kx.For example, maybe y = 2x: this means that for every increase in x, y will increase by double that amount.You can see that the bigger the number you plug in for x, the bigger the resulting value of y will be.In this problem, we're trying to isolate a, so it makes more sense to put it all by itself on one side of the equation; this will make the math easier later on.Next, we have 'the sum of 3 and b, or in math terms, b 3 instead of plain old b.


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