A direct variation is a relationship that follows a specific format.
y= mx
In this form, m is the constant of variation and m≠0. Let's begin by determining whether a direct variation exists for the given data.
Does y Vary Directly?
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 determine m for each ( x, y) pair. If m is the same for all four pairs, we can conclude that direct variation exists.
x
y
y/x
m
- 1
-6
-6/- 1
6
2
3
3/2
3/2
5
12
12/5
12/5
9
24
24/9
8/3
Notice that for all four pairs, m has a different value. Therefore, y does not vary directly with x.
