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In a direct variation, $y=15$ when $x=5$ . 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 and solve direct variation equations

Full solution

Q. In a direct variation,

y=15

when

x=5

. 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 Equation: Identify the equation that represents direct variation. $\newline$ Direct variation means $y$ is directly proportional to $x$ . $\newline$ The general form of direct variation is $y = kx$ , where $k$ is the constant of variation.
Find Constant: Use the given values to find the constant of variation $k$ . We are given that $y = 15$ when $x = 5$ . Substitute these values into the direct variation equation $y = kx$ . $15 = k \times 5$
Solve for $k$ : Solve for the constant of variation ( $k$ ). $\newline$ To find $k$ , divide both sides of the equation by $5$ . $\newline$ $\frac{15}{5} = \frac{(k \times 5)}{5}$ $\newline$ $3 = k$
Write Equation: Write the direct variation equation using the found value of $k$ . Now that we know $k = 3$ , substitute it back into the general form $y = kx$ . The direct variation equation is $y = 3x$ .

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