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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 $y$ . Write your answer as an equation with $y$ first, followed by an equals sign.

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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

. 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: $\newline$ $y = 3x$

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