A direct variation is a relationship that follows a specific format.
y= kx
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 direct variation exists. Start by solving the general direct variation equation for k.
y= kx ⇒ k=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
y/x
k
2
-1
-1/2
- 1/2 âś“
4
-2
- 2/4
- 1/2 âś“
6
-3
-3/6
- 1/2 âś“
Notice that for all three pairs, k=- 12. Therefore, y varies directly with x. Now that we know direct variation exists, we can write a function rule in the form y= kx.
y= -1/2x
