If $y$ varies directly with $x$ , and if $y = 12$ when $x = 3$ , how do you write the direct variation equation?

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Solution

Finding direct variation of $y$ with $x$ :
Given, $y$ varies directly with $x$ .
i.e. $y α x$
$\Rightarrow y = k x (k = proportionalityconstant) \dots (1)$
Given, $y = 12$ and $x = 3$ .
Put the values in $(1)$ .
$\Rightarrow 12 = k \times 3 \Rightarrow k = 4$
So from equation $(1)$ , we have
$y = 4 x$
Thus, the direct variation equation is $y = 4 x$ .

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If y varies directly with x, and if y=12 when x=3, how do you write the direct variation equation?

Finding direct variation of y with x :Given, y varies directly with x.i.e. yαx⇒y=kx(k=proportionalityconstant)…(1)Given, y=12 and x=3.Put the values in (1).⇒12=k×3⇒k=4So from equation (1), we have y=4xThus, the direct variation equation is y=4x.

If $y$ varies directly with $x$ , and if $y = 12$ when $x = 3$ , how do you write the direct variation equation?