If $y$ varies directly with $x$ , if $y = - 9$ when $x = 3$ , how do you find $y$ when $x = - 5$ ?

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Solution

Find the value $y$ when $x = - 5$ :
Given: $y_{1} = - 9$ when $x_{1} = 3$ .
As $y$ varies directly with $x$ , this can be obtained:
$\frac{y_{1}}{x_{1}} = \frac{y}{x}$
Putting $y_{1}$ as $- 9$ , $x_{1}$ as $3$ and $x$ as $- 5$ :
$\begin{array}{rcl} - \frac{9}{3} & = & \frac{y}{- 5} \\ \Rightarrow & 3 y = 45 \\ \Rightarrow & y = 15 \end{array}$
Hence, the value of $y$ is $15$ when $x$ is $- 5$ .

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