The constant of variation in a <span>direct variation </span>is the constant (unchanged) ratio of two <span>variable </span>quantities.
The formula for direct variation is
<span><span>y=kx </span></span>(or <span><span>y=kx</span></span>)
where <span>kk</span> is the constant of variation.
Example 1:
If <span>y</span> varies directly as <span>x</span> and <span><span>y=15</span></span> when x=24,
find <span>x</span> when <span><span>y=25</span></span> .
Find the constant of variation.
<span><span><span>k=<span>y/x</span>=<span>15/24</span>=<span>5/</span></span></span></span>8y=5/8x
To find <span>x</span>, substitute <span>25</span> for y.
25=5/8x
<span><span><span>x=40</span></span></span>
The constant of variation in an <span>indirect variation </span>is the constant (unchanged) product between two variable quantities.
The formula for indirect variation is
<span><span>xy=k </span></span>(or <span><span>y=<span>k/x</span></span></span> )
where <span>k</span> is the constant of variation .
Example 2:
If it takes <span>4</span> hours at an average speed of <span>90</span> km/h to do a certain journey, how long would it take at <span>120</span> km/h?
Find the constant of variation.
<span>k</span> = speed · time
<span><span>k=90⋅4=360</span></span>
Then,
<span><span><span>time=<span>k/speed</span></span><span> =<span>360/120</span></span><span> =3 hours.</span></span></span>
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