If y varies inversely with x and y = 3 when x = 6 , find y when x = 2 . Write and solve an inverse variation equation to find the answer. y = _____

Given Inverse Variation Equation: Given that y varies inversely with x, we can write the inverse variation equation as y = k / x, where k is the constant of variation.Substitute Values: We know that y = 3 when x = 6. Substitute these values into the inverse variation equation to find the constant k. 3 = k / 6Find Constant k: To find k, multiply both sides of the equation by 6. 3 * 6 = k 18 = kWrite Inverse Variation Equation: Now that we have found the constant of variation k = 18, we can write the inverse variation equation as y = 18 / x.Find y for x=2: To find y when x = 2, substitute 2 for x in the equation y = 18 / x. y = 18 / 2 y = 9

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If $y$ varies inversely with $x$ and $y = 3$ when $x = 6$ , find $y$ when $x = 2$ . $\newline$ Write and solve an inverse variation equation to find the answer. $\newline$ $y =$ _____

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Algebra 1

Write and solve inverse variation equations

Full solution

Q. If

y

varies inversely with

x

and

y = 3

when

x = 6

, find

y

when

x = 2

\newline

Write and solve an inverse variation equation to find the answer.

\newline

y =

_____

Given Inverse Variation Equation: Given that $y$ varies inversely with $x$ , we can write the inverse variation equation as $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Substitute Values: We know that $y = 3$ when $x = 6$ . Substitute these values into the inverse variation equation to find the constant $k$ . $\newline$ $3 = \frac{k}{6}$
Find Constant $k$ : To find $k$ , multiply both sides of the equation by $6$ . $3 \times 6 = k$ $18 = k$
Write Inverse Variation Equation: Now that we have found the constant of variation $k = 18$ , we can write the inverse variation equation as $y = \frac{18}{x}$ .
Find $y$ for $x=2$ : To find $y$ when $x = 2$ , substitute $2$ for $x$ in the equation $y = \frac{18}{x}$ .
$y = \frac{18}{2}$
$y = 9$