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}\\\\ -------------------------------\\\\ (\stackrel{x}{5}~,~\stackrel{y}{8})\textit{ we also know that } \begin{cases} x=5\\ y=8 \end{cases}\implies 8=k5\implies \cfrac{8}{5}=k[/tex]
calculista

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]

where

k is the constant of variation

in this problem we have

the point [tex](5,8)[/tex]

so

[tex]x=5\\y=8[/tex]

substitute

[tex]\frac{y}{x}=k[/tex]

[tex]\frac{8}{5}=k[/tex]

therefore

the answer is

[tex]k=\frac{8}{5}[/tex]

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