Question

Tell me which situation has the correct equation and representation and inverse variation

Answer 1

Let's begin by listing out the given information:

Direct variation refers to the relationship between two variables such that one variable is equivalent to the product of a constant & the other variable. Such that, an increase in one variable produces a commensurate increase in the second variable & a decrease in one variable produces a commensurate decrease in the other variable

Mathematically,

$x\alpha y\Rightarrow x=k\cdot y$

Indirect variation refers to a relationship between two variables such that an increase in one variable produces a decrease in the second variable & a decrease in one variable produces a commensurate decrease in the other variable

Mathematically,

$x\alpha\frac{1}{y}\Rightarrow x=\frac{k}{y}$

Looking at the picture, we will observe that:

Situation 1 is a direct variation (the more people sign up with the local league, the more money is generated)

Situation 2 is an indirect variation (the more money a student raises. the lesser the loan to take out)

$\begin{gathered} 10,000M\alpha\frac{1}{5}L\Rightarrow10,000M=\frac{1}{5}L \\ L=10,000(5)=50,000M \\ \therefore M=\frac{50,000}{L} \end{gathered}$

Situation 2 is inverse variation because M = 50,000/L