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In a direct variation, $y = 18$ 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.

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Write and solve direct variation equations

Full solution

Q. In a direct variation,

y = 18

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.

Identify General Form: Identify the general form of direct variation. $\newline$ The general form of direct variation is $y = k \times x$ , where $k$ is the constant of variation.
Substitute Values: Substitute $y = 18$ and $x = 2$ into the equation $y = k \times x$ . $\newline$ $y = k \times x$ $\newline$ $18 = k \times 2$
Solve for Constant: Solve the equation for the constant of variation, $k$ . $\frac{18}{2} = \frac{(k \times 2)}{2}$ $k = 9$
Substitute into Formula: Substitute the value of $k$ into the direct variation formula. $\newline$ Substitute $k = 9$ in $y = k \times x$ . $\newline$ $y = 9x$

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