Assume that y varies inversely with x. If y = 2 when x = 9 , find y when x = 3 . Write and solve an inverse variation equation to find the answer. y = _____

Understand Relationship: Understand the relationship between y and x. Since y varies inversely with x, the relationship can be described by the equation y = k / x, where k is the constant of variation.Find Constant of Variation: Use the given values to find the constant of variation k. We are given that y = 2 when x = 9. Substitute these values into the inverse variation equation to find k. 2 = k / 9 Now, solve for k by multiplying both sides by 9. 2 * 9 = k k = 18Write Inverse Variation Equation: Write the inverse variation equation with the found value of k. Now that we have found k to be 18, the inverse variation equation is y = 18 / x.Find y for x=3: Find y when x = 3 using the inverse variation equation. Substitute x = 3 into the equation y = 18 / x. y = 18 / 3 y = 6

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Assume that $y$ varies inversely with $x$ . If $y = 2$ when $x = 9$ , find $y$ when $x = 3$ . $\newline$ 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. Assume that

y

varies inversely with

x

. If

y = 2

when

x = 9

, find

y

when

x = 3

\newline

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

\newline

y =

_____

Understand Relationship: Understand the relationship between $y$ and $x$ . Since $y$ varies inversely with $x$ , the relationship can be described by the equation $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find Constant of Variation: Use the given values to find the constant of variation $k$ . We are given that $y = 2$ when $x = 9$ . Substitute these values into the inverse variation equation to find $k$ . $2 = \frac{k}{9}$ Now, solve for $k$ by multiplying both sides by $9$ . $2 \times 9 = k$ $k = 18$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we have found $k$ to be $18$ , the inverse variation equation is $y = \frac{18}{x}$ .
Find $y$ for $x=3$ : Find $y$ when $x = 3$ using the inverse variation equation. $\newline$ Substitute $x = 3$ into the equation $y = \frac{18}{x}$ . $\newline$ $y = \frac{18}{3}$ $\newline$ $y = 6$