Question

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what is the direct variation equation for the table of ordered pares x 60 70 80 y 48 56 64

what is the direct variation equation for the table of ordered pares
x 20 30 40 y 24 36 48

Answer 1

`\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} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ \stackrel{Table~A}{\begin{array}{ccll} x&y\\ \cline{1-2} 60&48\\70&56\\80&64 \end{array}}~\hspace{7em} \stackrel{Table~B}{\begin{array}{ccll} x&y\\ \cline{1-2} 20&24\\30&36\\40&48 \end{array}} \\\\[-0.35em] ~\dotfill`

`\bf \textit{for table A, we know that } \begin{cases} x=60\\ y=48 \end{cases}\implies 48=k60\implies \cfrac{48}{60}=k \\\\\\ \cfrac{4}{5}=k\qquad therefore\qquad \boxed{y=\cfrac{4}{5}x} \\\\\\ \textit{for table B, we know that } \begin{cases} x=30\\ y=36 \end{cases}\implies 36=k30\implies \cfrac{36}{30}=k \\\\\\ \cfrac{6}{5}=k\qquad therefore\qquad \boxed{y=\cfrac{6}{5}x}`