** ** **Write an equation expressing direct Variation** ** ** ** **

The circumference of a circle is given by the formula *C = *2p*r*, where *r *is the radius of the circle. See the figure. Circumference is always a constant multiple of the radius. (*C *is always found by multiplying *r *by the constant 2p.) Thus, As the *radius increases, *the *circumference increases*. The reverse is also true. As the *radius decreases, *the *circumference decreases*. Because of this, the circumference is said to *vary directly *as the radius. **Direct Variation**

** ** *y *varies directly as *x *if there exists some constant *k *such that *y * = *kx*. Also, *y *is said to be **proportional to ***x*.

The number *k *is called the **constant** **of variation. **In direct variation, for *k *> 0, as the value of *x *increases, the value of *y *also increases. Similarly, as *x *decreases, *y *decreases.