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. Before we can write a direct variation equation, we should first find out if direct variation exists.
Does y Vary Directly?
Solving the general direct variation equation for m, we have the following.
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 three pairs, we can conclude that direct variation exists.
x
y
y/x
m
- 2
1
1/- 2
- 1/2
3
6
6/3
2
8
11
11/8
11/8
Notice that m is different for each pair. Therefore, y does not vary directly with x.
Checking Our Answer
We can check our answer by plotting the points and sketching a line through them. If one straight line crosses through all of the points, as well as the origin, it is a direct variation equation.
We can see that one line crossed through all three points but not through the origin. Therefore, it is not a direct variation equation.
