Assume that y varies inversely with x. If y = 4 when x = 3 , find y when x = 1 . Write and solve an inverse variation equation to find the answer. y = _____

Understand relationship between y and x: Understand the relationship between y and x. Inverse variation means that y is directly proportional to the reciprocal of x. The general form of an inverse variation is y = k / x, where k is the constant of variation.Find constant of variation k: Use the given values to find the constant of variation k. We are given that y = 4 when x = 3. Substitute these values into the inverse variation formula to find k. 4 = k / 3 Now, solve for k by multiplying both sides by 3. 4 * 3 = k 12 = kWrite inverse variation equation: Write the inverse variation equation with the found constant k. Now that we have found k to be 12, we can write the inverse variation equation as y = 12 / x.Find y when x = 1: Find y when x = 1. Substitute x = 1 into the inverse variation equation y = 12 / x. y = 12 / 1 y = 12

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Assume that $y$ varies inversely with $x$ . If $y = 4$ when $x = 3$ , find $y$ when $x = 1$ . $\newline$ 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 = 4

when

x = 3

, find

y

when

x = 1

\newline

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

\newline

y =

_____

Understand relationship between y and x: Understand the relationship between y and x. $\newline$ Inverse variation means that $y$ is directly proportional to the reciprocal of $x$ . The general form of an inverse variation is $y = \frac{k}{x}$ , where $k$ is the constant of variation.
Find constant of variation $k$ : Use the given values to find the constant of variation $k$ . We are given that $y = 4$ when $x = 3$ . Substitute these values into the inverse variation formula to find $k$ . $4 = \frac{k}{3}$ Now, solve for $k$ by multiplying both sides by $3$ . $4 \times 3 = k$ $12 = k$
Write inverse variation equation: Write the inverse variation equation with the found constant $k$ . Now that we have found $k$ to be $12$ , we can write the inverse variation equation as $y = \frac{12}{x}$ .
Find $y$ when $x = 1$ : Find $y$ when $x = 1$ . Substitute $x = 1$ into the inverse variation equation $y = \frac{12}{x}$ . $y = \frac{12}{1}$ $y = 12$