How do you write the equation of a direct variation that includes the point (-6,1)?

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How do you write the equation of a direct variation that includes the point (-6,1)?

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Answer 1 · 2016-03-09T15:24:24

Equation of direct variation is: $y = (- \frac{1}{6}) x$ $" "y=(-1/6)x$

Explanation:

Let $(x, y) \to (- 6, 1)$ $(x,y) ->(-6,1)$

The term 'direct variation implies that we have the structure of

Let $k$ $k$ be a constant of variation

Then $y = k x$ $y=kx$ ....................(1)

We are given that $(x, y) \to (- 6, 1)$ $(x,y)->(-6,1)$ so by substitution equation (1) becomes

$1 = k (- 6)$ $1=k(-6)$

Divide both sides by -6

$\frac{1}{- 6} = k \times \frac{- 6}{- 6}$ $1/(-6)=kxx(-6)/(-6)$

But $\frac{- 6}{- 6} = 1$ $(-6)/(-6)=1$ giving

$- \frac{1}{6} = k$ $-1/6=k$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Equation of direct variation is: $y = k x \to y = (- \frac{1}{6}) x$ $" "y = kx" "->" "y=(-1/6)x$

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How do you write the equation of a direct variation that includes the point (-6,1)?

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