Respuesta :
[tex]\bf \qquad \qquad \textit{direct proportional variation}\\\\
\textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby
\begin{array}{llll}
k=constant\ of\\
\qquad variation
\end{array}\\\\
-------------------------------\\\\
\textit{we know that }
\begin{cases}
y=10\\
x=5
\end{cases}\quad 10=k5\implies \cfrac{10}{5}=k\implies 2=k[/tex]
Answer: The required value of k is 2.
Step-by-step explanation: Given that y varies directly as x and y = 10 when x = 5.
We are to find the value of k, the constant of variation.
According to the given information, we have
[tex]y\propto x\\\\ \Righatrrow y=k\times x\\\\ \Rightarrow y=kx[/tex]
y = 10 when x = 5, so we get from above equation
[tex]10=k\times 5\\\\\Rightarrow k=\dfrac{10}{5}\\\\\Rightarrow k=2.[/tex]
Thus, the required value of k is 2.
