A direct variation is another name for a proportional relationship and it 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 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 m for each ( x, y)-coordinate pair. If m is the same for all three pairs, we will know for certain that a direct variation exists.
x
y
y/x
m
- 2
1
1/- 2
- 1/2
2
- 1
- 1/2
- 1/2
4
- 2
- 2/4
- 1/2
Notice that the value of m for all three pairs is - 12. This means that y does vary directly with x. Now that we know that a direct variation exists, we can write a direct variation equation in the form y= mx.
y= -1/2x
Extra
What It Means
What does a constant of variation of - 12 mean? A constant of variation tells us how many units we move up or down each time we move to the right. We can think of this fraction as the change in y divided by the change in x.
Change iny/Change inx=-1/2
This function moves 1 step down, because it is a negative number, each time it moves 2 steps to the right.
