Question

The value of y varies directly with x, and y = 343 when x = 49. Find y when x = 8

Answer 1

$\bf \qquad \qquad \textit{direct proportional variation} \\\\ \textit{\underline{y} varies directly with \underline{x}}\qquad \qquad y=kx\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array}\\\\ -------------------------------\\\\ \textit{we also know that } \begin{cases} y=343\\ x=49 \end{cases}\implies 343=k49\implies \cfrac{343}{49}=k \\\\\\ 7=k\qquad therefore\qquad \boxed{y=7x} \\\\\\ \textit{when x = 8, what is \underline{y}?}\qquad y=7(8)\implies y=56$