Exercise 23 Page 88

A direct variation is another name for a proportional relationship and it 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 a direct variation exists for this relation. We will start by solving the general direct variation equation for

m .

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

To determine if

y

varies directly with

x

for the given relationship, we must find the value of

k

for each

(x, y) -

coordinate pair. If

k

is the same for all four pairs, we will know for certain that a direct variation exists.

Hours, $x$	Miles, $y$	$\frac{y}{x}$	$k$
$3$	$108$	$\frac{1 0 8}{3}$	$36$
$5$	$180$	$\frac{1 8 0}{5}$	$36$
$7$	$252$	$\frac{2 5 2}{7}$	$36$
$9$	$324$	$\frac{3 2 4}{9}$	$36$

Notice that the value of $k$ for all pairs is $36 .$ This means that $y$ does vary directly with $x,$ and the constant of proportionality equals $36 .$