In a direct variation, y = 9 when x = 3. Write a direct variation equation that shows the relationship between x and y. Write your answer as an equation with y first, followed by an equals sign. ____

Identify Form: Identify the form of the direct variation equation. Direct variation means y varies directly with x, which can be represented by the equation y = kx, where k is the constant of variation.Find Constant: Use the given values to find the constant of variation k. We are given that y = 9 when x = 3. We can substitute these values into the direct variation equation to find k. 9 = k * 3Solve for k: Solve for k. To find k, we divide both sides of the equation by 3. k = 9 / 3 k = 3Write Equation: Write the direct variation equation using the value of k. Now that we have found k to be 3, we can write the direct variation equation as: y = 3x

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In a direct variation, $y = 9$ when $x = 3$ . Write a direct variation equation that shows the relationship between $x$ and $y$ . $\newline$ Write your answer as an equation with $y$ first, followed by an equals sign.

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Algebra 1

Write direct variation equations

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Q. In a direct variation,

y = 9

when

x = 3

. Write a direct variation equation that shows the relationship between

x

and

y

\newline

Write your answer as an equation with

y

first, followed by an equals sign.

Identify Form: Identify the form of the direct variation equation. $\newline$ Direct variation means $y$ varies directly with $x$ , which can be represented by the equation $y = kx$ , where $k$ is the constant of variation.
Find Constant: Use the given values to find the constant of variation $k$ . We are given that $y = 9$ when $x = 3$ . We can substitute these values into the direct variation equation to find $k$ . $9 = k \times 3$
Solve for k: Solve for k. $\newline$ To find k, we divide both sides of the equation by $3$ . $\newline$ $k = \frac{9}{3}$ $\newline$ $k = 3$
Write Equation: Write the direct variation equation using the value of $k$ . $\newline$ Now that we have found $k$ to be $3$ , we can write the direct variation equation as: $\newline$ $y = 3x$