Assume that y varies inversely with x. If y = 1 when x = 8 , find y when x = 4 . Write and solve an inverse variation equation to find the answer. y = _____

Understand Relationship: Understand the relationship between y and x. Inverse variation means that as one variable increases, the other decreases proportionally. The formula for inverse variation is 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 = 1 when x = 8. Substitute these values into the inverse variation formula to find k. 1 = k / 8 Multiply both sides by 8 to solve for k. 1 * 8 = k k = 8Write Inverse Variation Equation: Write the inverse variation equation with the found constant k. Now that we know k = 8, the inverse variation equation is y = 8 / x.Find Value of y: Find the value of y when x = 4. Substitute x = 4 into the inverse variation equation y = 8 / x. y = 8 / 4 y = 2

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Assume that $y$ varies inversely with $x$ . If $y = 1$ when $x = 8$ , 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. Assume that

y

varies inversely with

x

. If

y = 1

when

x = 8

, find

y

when

x = 4

\newline

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

\newline

y =

_____

Understand Relationship: Understand the relationship between $y$ and $x$ . Inverse variation means that as one variable increases, the other decreases proportionally. The formula for inverse variation is $y = \frac{k}{x}$ , 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 $y = 1$ when $x = 8$ . Substitute these values into the inverse variation formula to find $k$ . $1 = \frac{k}{8}$ Multiply both sides by $8$ to solve for $k$ . $1 \times 8 = k$ $k = 8$
Write Inverse Variation Equation: Write the inverse variation equation with the found constant $k$ . Now that we know $k = 8$ , the inverse variation equation is $y = \frac{8}{x}$ .
Find Value of $\newline$ $y$ : Find the value of $\newline$ $y$ when $\newline$ $x = 4$ . $\newline$ Substitute $\newline$ $x = 4$ into the inverse variation equation $\newline$ $y = \frac{8}{x}$ . $\newline$ $\newline$ $y = \frac{8}{4}$ $\newline$ $\newline$ $y = 2$