What is the direct variation equation that goes through point (2,5)?

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Answer 1 · 2017-05-03T19:53:28

$y = \frac{5}{2} x$ $y=5/2x$

Picking the word 'direct' we have the situation $y . α . x$ $y color(white)(.)alpha color(white)(.) x$

where $α$ $alpha$ means proportional to

Let $k$ $k$ be the constant of variation giving:

$y = k x$ $y=kx$

Using $k$ $k$ permits us to change $α$ $alpha$ to the equals sign

We have the 'initial condition' of the 'ordered pair' $(x, y) \to (2, 5)$ $(x,y)->(2,5)$

$\Rightarrow y = k x \to 5 = k (2)$ $=>" "y=kx" "->" "5=k(2)$

Thus $k = \frac{5}{2}$ $k=5/2$ giving:

$y = \frac{5}{2} x$ $y=5/2x$