Inverse Variation 1
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Question 1 of 4
1. Question
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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Incorrect
Inverse Variation Formula
$$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$$where `k≠0` and is the constant of variationRemember
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` -
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Question 2 of 4
2. Question
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)
Hint
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Correct!
Incorrect
Inverse Variation Formula
$$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$$where `k≠0` and is the constant of variationRemember
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` -
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Question 3 of 4
3. Question
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)
Hint
Help VideoCorrect
Keep Going!
Incorrect
Inverse Variation Formula
$$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$$where `k≠0` and is the constant of variationRemember
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` -
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Question 4 of 4
4. Question
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)
Hint
Help VideoCorrect
Fantastic!
Incorrect
Inverse Variation Formula
$$\color{#9a00c7}{y}=\frac{k}{\color{#004ec4}{x}}$$where `k≠0` and is the constant of variationRemember
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` -