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In a direct variation, $y = 20$ 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 = 20

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 $y = 20$ and $x = 2$ into the equation $y = k \times x$ . $\newline$ $20 = k \times 2$
Solve for constant: Solve the equation for the constant of variation, $k$ . $\frac{20}{2} = \frac{(k \times 2)}{2}$ $k = 10$
Substitute into formula: Substitute the value of $k$ into the direct variation formula. $\newline$ Substitute $k = 10$ in $y = k \times x$ . $\newline$ $y = 10x$

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