Assume that y varies inversely with x. If y = 2 when x = 12 , find y when x = 3 . Write and solve an inverse variation equation to find the answer. y = _____

Given Relationship Formula: Given that y varies inversely with x, we can express this relationship using the formula y = k / x, where k is the constant of variation. To find the constant k, we use the given values y = 2 when x = 12. Substitute these values into the formula to get 2 = k / 12. Now, solve for k by multiplying both sides by 12 to isolate k. 2 * 12 = k 24 = kFind Constant k: Now that we have found the constant of variation k to be 24, we can write the inverse variation equation as y = 24 / x. To find the value of y when x = 3, substitute 3 for x in the equation. y = 24 / 3 y = 8

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Assume that $y$ varies inversely with $x$ . If $y = 2$ when $x = 12$ , 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 = 12

, find

y

when

x = 3

\newline

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

\newline

y =

_____

Given Relationship Formula: Given that $y$ varies inversely with $x$ , we can express this relationship using the formula $y = \frac{k}{x}$ , where $k$ is the constant of variation. $\newline$ To find the constant $k$ , we use the given values $y = 2$ when $x = 12$ . $\newline$ Substitute these values into the formula to get $2 = \frac{k}{12}$ . $\newline$ Now, solve for $k$ by multiplying both sides by $12$ to isolate $k$ . $\newline$ $x$ $1$ $\newline$ $x$ $2$
Find Constant $k$ : Now that we have found the constant of variation $k$ to be $24$ , we can write the inverse variation equation as $y = \frac{24}{x}$ . To find the value of $y$ when $x = 3$ , substitute $3$ for $x$ in the equation. $y = \frac{24}{3}$ $y = 8$