Direct Variation:

$y$ varies directly with $x$ with a constant variation of $k$

$y = kx$

where$k \neq$ 0

$y$ varies directly with $x$ with a constant variation of $k$

where

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Examples

**Identifying direct variations by table of values**

Do the following tables of values represent direct variation?

**Identifying direct variations**

Which of the following represent direct variation?

A. $y$ = 2

B. $y$ = 3.1$x$

C. $y = - \frac{7x}{9}$

D. $xy$ = 191

E. $y$ = 8$x$ + 5

- Variable $y$ varies directly with $x$. Determine $m$ and $n$

- If $a$ varies directly as $b$, and $b$ = 4 when $a$ = 16, find $a$ when $b = \frac{3}{2}$
- If the volume of an object varies directly as the cube of its height, and the volume equals 40$ft^{3}$ when the height is 2$ft$, find the object's volume when its height equals $\frac{1}{3} ft$