Question

1. If f(x) varies directly with x, and f(x) = 12 when x = 8, write the direct linear variation equation.

Answer 1

$1.\ f(x)=mx\\\\f(x)=12\ when\ x=8\\\\therefore:\\\\m\cdot8=12\ \ \ |divide\ both\ sides\ by\ 8\\\\m=\frac{12}{8}\\\\m=\frac{3}{2}\\\\\boxed{d.\ f(x)=\frac{3}{2}x}$

$2.\ y=mx\\\\\boxed{b.\ y=\frac{6}{x}}\\\\other\ are\ ok:\\\\a.\ y=5x\to m=5\\c.\ y=0.7x\to m=0.7\\d.\ y=\frac{x}{9}=\frac{1}{9}x\to m=\frac{1}{9}$

$3.\\m=\frac{y}{x}\\\\x=1\ and\ y=3\to\ m=\frac{3}{1}=3\\\\x=2\ and\ y=6\to m=\frac{6}{2}=3\\\\x=3\ and\ y=9\to m=\frac{9}{3}=3\\\\x=4\ and\ y=12\to m=\frac{12}{4}=3\\\\Answer:\boxed3$