Question

The value of y directly varies with x, and y=5.4 when x =9. Find y when x= negative 10

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}\\\\ -------------------------------`


`\bf \textit{we also know that } \begin{cases} y=5.4\\ x=9 \end{cases}\implies 5.4=k9\implies \cfrac{5.4}{9}=k \\\\\\ \cfrac{\quad (54)/(10)\quad }{9}=k\implies \cfrac{54}{10}\cdot \cfrac{1}{9}=k\implies \cfrac{3}{5}=k\qquad thus\qquad \boxed{y=\cfrac{3}{5}x} \\\\\\ \textit{when x = -10, what is \underline{y}?}\qquad y=\cfrac{3}{5}(-10)`