Inverse Variation 1

Question 1 of 4

Given the following, find the equation for the inverse variation and then solve for the missing

$y$ value

$y=8$ when

$x=-4$

$y=?$ when

$x=6$

Write fractions in the format “a/b”

$(i)$ Equation: $y=$ (-32/x)

$(ii)$ Missing value: $y=$ (-5 1/3)

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Inverse Variation Formula

$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$

where

$k≠0$ and is the constant of variation

Remember

An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.

First, solve for

$k$ , the constant of variation, by plugging in the known values to the Inverse Variation Formula.

$y$	$=$	$8$
$x$	$=$	$-4$

$y$	$=$	$\frac{k}{\color{#004ec4}{x}}$	Inverse Variation Formula

$8$	$=$	$\frac{k}{\color{#004ec4}{-4}}$	Substitute known values

$8$ $times-4$	$=$	$k/(-4)$ $times-4$	Multiply $-4$ to both sides

$-32$	$=$	$k$
$k$	$=$	$-32$

Next, rewrite the Inverse Variation Formula with

$k$ substituted.

$y$	$=$	$k/x$

$y$	$=$	$(-32)/x$	Substitute $k$

Finally, use the new formula and substitute

$x=6$

$y$	$=$	$(-32)/x$	New formula

$y$	$=$	$(-32)/6$	Substitute $x=6$

$y$	$=$	$-5 1/3$

$(i)$ Equation:

$y=(-32)/x$

$(ii)$ Missing value:

$y=-5 1/3$

Question 2 of 4

Given the following, find the equation for the inverse variation and then solve for the missing

$x$ value

$y=9.5$ when

$x=-1$

$y=-0.5$ when

$x=?$

Write fractions in the format “a/b”

$(i)$ Equation: $y=$ (-9.5/x)

$(ii)$ Missing value: $x=$ (19)

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Inverse Variation Formula

$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$

where

$k≠0$ and is the constant of variation

Remember

An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.

First, solve for

$k$ , the constant of variation, by plugging in the known values to the Inverse Variation Formula.

$y$	$=$	$9.5$
$x$	$=$	$-1$

$y$	$=$	$\frac{k}{\color{#004ec4}{x}}$	Inverse Variation Formula

$9.5$	$=$	$\frac{k}{\color{#004ec4}{-1}}$	Substitute known values

$9.5$ $times-1$	$=$	$k/(-1)$ $times-1$	Multiply $-1$ to both sides

$-9.5$	$=$	$k$
$k$	$=$	$-9.5$

Next, rewrite the Inverse Variation Formula with

$k$ substituted.

$y$	$=$	$k/x$

$y$	$=$	$(-9.5)/x$	Substitute $k$

Finally, use the new formula and substitute

$y=-0.5$

$y$	$=$	$(-9.5)/x$	New formula

$-0.5$	$=$	$(-9.5)/x$	Substitute $y=-0.5$

$-0.5$ $times x$	$=$	$(-9.5)/x$ $times x$	Multiply $x$ to both sides

$-0.5x$	$=$	$(-9.5)$
$-0.5x$ $divide-0.5$	$=$	$(-9.5)$ $divide-0.5$	Divide both sides by $0.5$
$x$	$=$	$19$

$(i)$ Equation:

$y=(-9.5)/x$

$(ii)$ Missing value:

$x=19$

Question 3 of 4

Given the following, find the equation for the inverse variation and then solve for the missing

$x$ value

$y=6.8$ when

$x=4.2$

$y=3$ when

$x=?$

Write fractions in the format “a/b”

$(i)$ Equation: $y=$ (28.56/x)

$(ii)$ Missing value: $x=$ (9.52)

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Inverse Variation Formula

$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$

where

$k≠0$ and is the constant of variation

Remember

An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.

First, solve for

$k$ , the constant of variation, by plugging in the known values to the Inverse Variation Formula.

$y$	$=$	$6.8$
$x$	$=$	$4.2$

$y$	$=$	$\frac{k}{\color{#004ec4}{x}}$	Inverse Variation Formula

$6.8$	$=$	$\frac{k}{\color{#004ec4}{4.2}}$	Substitute known values

$6.8$ $times4.2$	$=$	$k/(4.2)$ $times4.2$	Multiply $4.2$ to both sides

$28.56$	$=$	$k$
$k$	$=$	$28.56$

Next, rewrite the Inverse Variation Formula with

$k$ substituted.

$y$	$=$	$k/x$

$y$	$=$	$(28.56)/x$	Substitute $k$

Finally, use the new formula and substitute

$y=3$

$y$	$=$	$(28.56)/x$	New formula

$3$	$=$	$(28.56)/x$	Substitute $y=3$

$3$ $times x$	$=$	$(28.56)/x$ $times x$	Multiply $x$ to both sides

$3x$	$=$	$28.56$
$3x$ $divide3$	$=$	$28.56$ $divide3$	Divide both sides by $3$
$x$	$=$	$9.52$

$(i)$ Equation:

$y=(28.56)/x$

$(ii)$ Missing value:

$x=9.52$

Question 4 of 4

Given the following, find the equation for the inverse variation and then solve for the missing

$y$ value

$y=?$ when

$x=3$

$y=11$ when

$x=7$

Write fractions in the format “a/b”

$(i)$ Equation: $y=$ (77/x)

$(ii)$ Missing value: $y=$ (25 2/3)

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Inverse Variation Formula

$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$

where

$k≠0$ and is the constant of variation

Remember

An inverse variation is a relationship between two variables where if one decreases, the other increases. Similarly, if one variable increases, the other decreases.

First, solve for

$k$ , the constant of variation, by plugging in the known values to the Inverse Variation Formula.

$y$	$=$	$11$
$x$	$=$	$7$

$y$	$=$	$\frac{k}{\color{#004ec4}{x}}$	Inverse Variation Formula

$11$	$=$	$\frac{k}{\color{#004ec4}{7}}$	Substitute known values

$11$ $times7$	$=$	$k/(7)$ $times7$	Multiply $7$ to both sides

$77$	$=$	$k$
$k$	$=$	$77$

Next, rewrite the Inverse Variation Formula with

$k$ substituted.

$y$	$=$	$k/x$

$y$	$=$	$77/x$	Substitute $k$

Finally, use the new formula and substitute

$x=3$

$y$	$=$	$77/x$	New formula

$y$	$=$	$77/3$	Substitute $x=3$

$y$	$=$	$25 2/3$

$(i)$ Equation:

$y=77/x$

$(ii)$ Missing value:

$y=25 2/3$

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Quiz summary

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1. Question

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Inverse Variation Formula

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2. Question

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Inverse Variation Formula

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3. Question

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Inverse Variation Formula

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Inverse Variation Formula

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