In this form, k is the constant of variation and k≠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= mx ⇒ m=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.
Pictures, x
Profit, y
y/x
k
3
24
24/3
8
4
32
32/4
8
5
40
40/5
8
6
48
48/6
8
Notice that the value of k for all pairs is 8. This means that y does vary directly with x, and the constant of proportionality equals 8.
