Let y varies directly as x. If y = 12 when x = 4, then write a linear equation. What is value of y when x = 5?
Thinking Process
(i) Firstly, write the given condition as y ∝ x, then remove their proportionality sign by considering arbitrary constant k.
(ii) Secondly, substitute the value of x and y in the obtained equation and determine the value of k.
(iii) Further, substitute the value of k in obtained equation, to get the required equation.
Given that, $y$ varies directly as $x$.
i.e., $y \propto x \Rightarrow y=k x$ $\ldots(1)$
[where, $k=$ arbitrary constant]
Given, $y=12$ and $x=4$
$12=4 k$
$\Rightarrow$ $k=\frac{12}{4}$ [from Eq. (1)]
$\therefore^{2}+$ $k=3$
On putting the value of $k$ in Eq. (i), we get
$y=3 x$ .....(ii)
When $x=5$, then from Eq. (ii), we get
$y=3 \times 5 \Rightarrow y=15$
Hence, the value of $y$ is 15 .
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