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

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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

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

Explanation:

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

So it is an equation of a strait line.

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

So by substitution we have:

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

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

$\frac{1}{5} = k \times \frac{5}{5}$ $color(green)(1/(color(red)(5))=kxx 5/(color(red)(5)))$

But $\frac{5}{5} = 1 and k \times 1 = k$ $5/5=1 and kxx1=k$

$\frac{1}{5} = k$ $1/5=k$

So $y = k x \to y = \frac{1}{5} x \to y = \frac{x}{5}$ $y=kx" "->" "y=1/5x" "->" "y=x/5$

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

1 Answer

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