Assume that y varies inversely as x. If y = -6 when x = -2, how do you find y when x = 5?

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Assume that y varies inversely as x. If y = -6 when x = -2, how do you find y when x = 5?

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Answer 1 · 2016-04-05T09:38:24

At $x = 5; y = \frac{12}{5} = 2 \frac{2}{5}$ $x=5 "; "y=12/5 = 2 2/5$

Explanation:

This is a version ratios (ratios turn up all over the place).

Consider the example: $\frac{a}{b} = \frac{c}{d} \Rightarrow a = b \times \frac{c}{d}$ $a/b=c/d => a=bxxc/d$

This is exactly what we have in this question.

Let $k$ $k$ be a constant

$y = k \times \frac{1}{x}$ $y=kxx1/x$

$y = \frac{k}{x}$ $color(green)(y=k/x)$ ...................................(1)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$Determine the value of k$ $color(blue)("Determine the value of "k)$

Given condition: at $y = - 6 x = - 2$ $y=-6" "x=-2$

Substituting in equation (1)

$- 6 = \frac{k}{- 2}$ $" "-6=k/(-2)$

Multiply both sides by 2

$(- 6) \times 2 = k \times \frac{2}{- 2}$ $(-6)xx2=kxx 2/(-2)$

But $\frac{2}{- 2} = - 1$ $2/(-2)=-1$

$\Rightarrow - 12 = - k$ $=>-12=-k$

So $k = + 12$ $k=+12$

Thus equation (1) becomes

$y = \frac{12}{x}$ $color(green)(y=12/x)$ .................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

So at $x = 5$ $x=5$ we have:

$y = \frac{12}{5} = 2 \frac{2}{5}$ $" "y=12/5 = 2 2/5$

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Assume that y varies inversely as x. If y = -6 when x = -2, how do you find y when x = 5?

1 Answer

Explanation:

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