Exercise 1 Page 71

A direct variation is a relationship that follows a specific format.

y = k x

In this form,

k

is the constant of variation and

k \neq = 0 .

Before we can write a direct variation equation, we should first find out if direct variation exists. Start by solving the general direct variation equation for

k .

y = k x \Rightarrow k = \frac{y}{x}

To determine if

y

varies directly with

x

for the given relationship, we must determine

k

for each

(x, y)

pair. If

k

is the same for all three pairs, we can conclude that direct variation exists.

$x$	$y$	$\frac{y}{x}$	$k$
$2$	$- 1$	$\frac{- 1}{2}$	$- \frac{1}{2} ✓$
$4$	$- 2$	$\frac{- 2}{4}$	$- \frac{1}{2} ✓$
$6$	$- 3$	$\frac{- 3}{6}$	$- \frac{1}{2} ✓$

Notice that for all three pairs,

k = - \frac{1}{2} .

Therefore,

y

varies directly with

x .

Now that we know direct variation exists, we can write a function rule in the form

y = k x .

y = - \frac{1}{2} x