Question

Suppose y varies directly with x, and y = 14 when x = -4. What is the value if y when x = -6?

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \textit{we know that } \begin{cases} y=14\\ x=-4 \end{cases}\implies 14=k(-4)\implies \cfrac{14}{-4}=k\implies -\cfrac{7}{2}=k \\\\\\ therefore\qquad \boxed{y=-\cfrac{7}{2}x} \\\\\\ \textit{when x = -6, what is \underline{y}?}\qquad y=-\cfrac{7}{2}(-6)\implies y=21$