In a direct variation, y = 6 when x = 2. 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. ____

Understand direct variation: Understand the concept of direct variation. Direct variation means that y varies directly with x, which can be represented by the equation y = kx, where k is the constant of variation.Find constant of variation: Use the given values to find the constant of variation. We are given that y = 6 when x = 2. We can substitute these values into the direct variation equation to find k. 6 = k * 2Solve for k: Solve for the constant of variation k. To find k, we divide both sides of the equation by 2. k = 6 / 2 k = 3Write direct variation equation: Write the direct variation equation using the found constant of variation. Now that we know k = 3, we can write the direct variation equation as y = 3x.

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In a direct variation, $y = 6$ when $x = 2$ . 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 = 6

when

x = 2

. 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.

Understand direct variation: Understand the concept of direct variation. Direct variation means that $y$ varies directly with $x$ , which can be represented by the equation $y = kx$ , where $k$ is the constant of variation.
Find constant of variation: Use the given values to find the constant of variation. $\newline$ We are given that $y = 6$ when $x = 2$ . We can substitute these values into the direct variation equation to find $k$ . $\newline$ $6 = k \times 2$
Solve for k: Solve for the constant of variation $k$ . To find $k$ , we divide both sides of the equation by $2$ . $k = \frac{6}{2}$ $k = 3$
Write direct variation equation: Write the direct variation equation using the found constant of variation. $\newline$ Now that we know $k = 3$ , we can write the direct variation equation as $y = 3x$ .