If y varies inversely with x and y = 2 when x = 12 , find y when x = 4 . Write and solve an inverse variation equation to find the answer. y = _____

Understand Inverse Variation: Understand the concept of inverse variation. Inverse variation means that one variable increases as the other decreases. 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 = 12. Substitute these values into the inverse variation equation y = k / x. 2 = k / 12Solve for k: Solve for k. To find k, multiply both sides of the equation by 12. 2 * 12 = k 24 = kWrite Inverse Variation Equation: Write the inverse variation equation with the found value of k. Now that we know k = 24, the inverse variation equation is y = 24 / x.Find y: Find y when x = 4. Substitute x = 4 into the inverse variation equation y = 24 / x. y = 24 / 4 y = 6

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If $y$ varies inversely with $x$ and $y = 2$ when $x = 12$ , find $y$ when $x = 4$ . $\newline$ 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 = 2

when

x = 12

, find

y

when

x = 4

\newline

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

\newline

y =

_____

Understand Inverse Variation: Understand the concept of inverse variation. $\newline$ Inverse variation means that one variable increases as the other decreases. 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 $x = 12$ . Substitute these values into the inverse variation equation $y = \frac{k}{x}$ . $2 = \frac{k}{12}$
Solve for k: Solve for k. $\newline$ To find k, multiply both sides of the equation by $12$ . $\newline$ $2 \times 12 = k$ $\newline$ $24 = k$
Write Inverse Variation Equation: Write the inverse variation equation with the found value of $k$ . Now that we know $k = 24$ , the inverse variation equation is $y = \frac{24}{x}$ .
Find $y$ : Find $y$ when $x = 4$ . $\newline$ Substitute $x = 4$ into the inverse variation equation $y = \frac{24}{x}$ . $\newline$ $y = \frac{24}{4}$ $\newline$ $y = 6$