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In a direct variation, $y = 10$ 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 = 10

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 general form: Identify the general form of direct variation. $\newline$ General form of direct variation is $y = k \times x$ , where $k$ is the constant of variation.
Substitute values: Substitute $y = 10$ and $x = 5$ into the equation $y = k \times x$ . $\newline$ $10 = k \times 5$
Solve for constant: Solve the equation for the constant of variation, $k$ . $\frac{10}{5} = \frac{(k \times 5)}{5}$ $k = 2$
Substitute into formula: We have: $k = 2$ . Substitute the value of $k$ into the direct variation formula. $\newline$ Substitute $k = 2$ in $y = k \times x$ . $\newline$ $y = 2x$

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