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Direct variation describes an equation in which two variables are directly proportional, so when one increases, the other also increases.
The equation for direct variation is \(y=kx\). This means that for every \(1\) \(y\) increases, \(x\) increases by \(k\)
In the next example, you will see how to solve a direct variation problem. They are very formulaic and simple.
If ten dollars buys you twenty mangoes, how much does 3 dollars get you.
Since number of mangoes is greater than money, we will make money \(x\), and number of mangoes \(y\). Since we know that ten dollars gets you twenty mangoes, we can plug this into the formula to get $$10k = 20$$ Therefore \(k=2\). We can then plug this into the equation with three dollars to get $$y = 3*2$$ Therefore \(y=6\), so we can buy six mangoes.
Conlcusion:
You learned how to solve direct variation problems, which is the basis for linear functions.
Next: Average rate of change