How do you find the variation constant and an equation of variation where y varies inversely as x and y = 6 when x = 14?

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How do you find the variation constant and an equation of variation where y varies inversely as x and y = 6 when x = 14?

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Answer 1 · 2016-05-20T18:39:51

Variation constant is $84$ $84$

Explanation:

The maths symbol for proportional to is: $α$ $" "alpha$

Given that $y . α . \frac{1}{x}$ $" "y color(white)(.) alpha color(white)(.) 1/x$

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

$y = k \times \frac{1}{x} = \frac{k}{x}$ $y" "=" "kxx1/x" "=" "k/x$
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Given condition $if x = 14 then y = 6$ $color(blue)(" if "x=14" then "y=6)$

So by substitution

$y = \frac{k}{x} \to 6 = \frac{k}{14}$ $color(brown)(y=k/x" "->" "color(blue)(6)=k/(color(blue)(14))$

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Multiply both sides by $14$ $color(green)(14)$

$\Rightarrow 6 \times 14 = \frac{k}{14} \times 14$ $=>color(blue)(6color(green)(xx14) color(brown)(=) (color(brown)(k))/14color(green)(xx14))$

$\Rightarrow 84 = k \times \frac{14}{14}$ $=>84=kxx14/14$
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But $\frac{14}{14} = 1$ $14/14=1$

$84 = k \times 1$ $84=kxx1$

$k = 84 \to variation constant$ $color(magenta)(k=84 -> "variation constant")$

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So $y . α . \frac{1}{x} \to y = \frac{84}{x}$ $" "color(brown)(y color(white)(.) alpha color(white)(.) 1/x)" "->" "color(blue)(y=84/x)$

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How do you find the variation constant and an equation of variation where y varies inversely as x and y = 6 when x = 14?

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