Question

Suppose that y varies directly with x and y = 5 when x = 6. What is y when x = 5? I really need help with this.

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 also know that } \begin{cases} y=5\\ x=6 \end{cases}\implies 5=k6\implies \cfrac{5}{6}=k \\\\\\ therefore\qquad \boxed{y=\cfrac{5}{6}x} \\\\\\ \textit{when x = 5, what is \underline{y}?}\qquad y=\cfrac{5}{6}(5)\implies y=\cfrac{25}{6}\implies y=4(1)/(6)`