which equation is the direct variation equation if f(x) varies directly with x and f(x)=-9 when x = 3

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16-09-2017
Mathematics

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which equation is the direct variation equation if f(x) varies directly with x and f(x)=-9 when x = 3

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jdoe0001 jdoe0001 · Answer 1 · 2017-09-16T00:41:44+02:00

[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} \stackrel{f(x)}{y}=-9\\ x=3 \end{cases}\quad -9=k3\implies \cfrac{-9}{3}=k\implies \boxed{-3=k} \\\\\\ thus\qquad \qquad \stackrel{f(x)}{y}=-3x[/tex]