Inverse Variation 1

Question 1 of 4

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

y

$y$ value

y = 8

$y=8$ when

x = - 4

$x=-4$

y = ?

$y=?$ when

x = 6

$x=6$

Write fractions in the format “a/b”

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

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

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Inverse Variation Formula

y = \frac{k}{x}

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

where

k \neq 0

$k≠0$ 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

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

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

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

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

$8$ $8$ $\times - 4$ $times-4$	$=$ $=$	$\frac{k}{- 4}$ $k/(-4)$ $\times - 4$ $times-4$	Multiply $- 4$ $-4$ to both sides

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

Next, rewrite the Inverse Variation Formula with

k

$k$ substituted.

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

$y$ $y$	$=$ $=$	$\frac{- 32}{x}$ $(-32)/x$	Substitute $k$ $k$

Finally, use the new formula and substitute

x = 6

$x=6$

$y$ $y$	$=$ $=$	$\frac{- 32}{x}$ $(-32)/x$	New formula

$y$ $y$	$=$ $=$	$\frac{- 32}{6}$ $(-32)/6$	Substitute $x = 6$ $x=6$

$y$ $y$	$=$ $=$	$- 5 \frac{1}{3}$ $-5 1/3$

(i)

$(i)$ Equation:

y = \frac{- 32}{x}

$y=(-32)/x$

(i i)

$(ii)$ Missing value:

y = - 5 \frac{1}{3}

$y=-5 1/3$

Question 2 of 4

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

x

$x$ value

y = 9.5

$y=9.5$ when

x = - 1

$x=-1$

y = - 0.5

$y=-0.5$ when

x = ?

$x=?$

Write fractions in the format “a/b”

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

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

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Inverse Variation Formula

y = \frac{k}{x}

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

where

k \neq 0

$k≠0$ 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

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

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

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

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

$9.5$ $9.5$ $\times - 1$ $times-1$	$=$ $=$	$\frac{k}{- 1}$ $k/(-1)$ $\times - 1$ $times-1$	Multiply $- 1$ $-1$ to both sides

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

Next, rewrite the Inverse Variation Formula with

k

$k$ substituted.

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

$y$ $y$	$=$ $=$	$\frac{- 9.5}{x}$ $(-9.5)/x$	Substitute $k$ $k$

Finally, use the new formula and substitute

y = - 0.5

$y=-0.5$

$y$ $y$	$=$ $=$	$\frac{- 9.5}{x}$ $(-9.5)/x$	New formula

$- 0.5$ $-0.5$	$=$ $=$	$\frac{- 9.5}{x}$ $(-9.5)/x$	Substitute $y = - 0.5$ $y=-0.5$

$- 0.5$ $-0.5$ $\times x$ $times x$	$=$ $=$	$\frac{- 9.5}{x}$ $(-9.5)/x$ $\times x$ $times x$	Multiply $x$ $x$ to both sides

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

(i)

$(i)$ Equation:

y = \frac{- 9.5}{x}

$y=(-9.5)/x$

$(ii)$ 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:

$y=25 2/3$

Inverse Variation 1

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Quiz summary

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1. Question

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Great Work!

Inverse Variation Formula

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2. Question

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Correct!

Inverse Variation Formula

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3. Question

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Keep Going!

Inverse Variation Formula

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4. Question

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Fantastic!

Inverse Variation Formula

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