How do you write an equation of the direct variation that includes the given point (5, 1)?

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Answer 1 · 2017-03-29T09:49:04

$y=x/5$

Direct variation is of form $y=kx$ where $k$ is some constant.

So it is an equation of a strait line.

We may determine the value of $k$ as we are given values for $y and x$

So by substitution we have:

$(x,y)->y=kx->y=kxx x$
$(x,y)->color(white)(.)(5,1)color(white)(.)->1=kxx5$

Divide both sides by $color(red)(5)$ and we have:

$color(green)(1/(color(red)(5))=kxx 5/(color(red)(5)))$

But $5/5=1 and kxx1=k$

$1/5=k$

So $y=kx" "->" "y=1/5x" "->" "y=x/5$