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 k, 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
- 6
9
9/- 6
- 3/2
1
- 1.5
- 1.5/1
- 3/2
8
- 12
- 12/8
- 3/2
Notice that for all three pairs, m=- 32. Therefore, y varies 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 was able to cross through all three points. Therefore, it is a direct variation.
Equation
Now that we know a direct variation exists, we can write a direct variation equation of the form y= mx. Since m=- 32, the equation is as follows.
y= -3/2x
