Question

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

a.F(x)=8x
b.F(x)=12x
c.F(x)=2/3x
d.F(x)=3/2x

2.Which does not show a direct variation between x and y?

a.y=5x
b.y=6/x
c.y=0.7x
d.y=x/9

3.Find the constant of variation for the relationship shown in the following table:

x 1 2 3 4
y 3 6 9 12

Answer 1

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


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


`3.\\m=(y)/(x)\\\\x=1\ and\ y=3\to\ m=(3)/(1)=3\\\\x=2\ and\ y=6\to m=(6)/(2)=3\\\\x=3\ and\ y=9\to m=(9)/(3)=3\\\\x=4\ and\ y=12\to m=(12)/(4)=3\\\\Answer:\boxed3`