Question

Write an equation of the direct variation that includes the point (-10,-17)

Answer 1

$\bf \begin{array}{rllll} (-10&,&-17)\\ x&&y \end{array}\\\\ -------------------------------\\\\ \qquad \qquad \textit{direct proportional variation}\\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ variation \end{array}\\\\ -------------------------------$

$\bf \textit{we know that } \begin{cases} x=-10\\ y=-17 \end{cases}\implies -17=-10k\implies \cfrac{-17}{-10}=k \\\\\\ \cfrac{17}{10}=k\implies {1\frac{7}{10}=k} \\\\\\ thus\qquad \qquad y=1\frac{7}{10}x$