How can you determine if a relationship is a direct variation using values from the table?
Varies Directly? No
Practice makes perfect
A direct variation is another name for a proportional relationship and it follows a specific format.
y= kxIn 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 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 k for each ( x, y)-coordinate pair. If k is the same for all four pairs, we will know for certain that a direct variation exists.
Age, x
Grade, y
y/x
k
11
5
5/11
5/11
13
7
7/13
7/13
15
9
9/15
9/15
19
11
11/19
11/19
Notice that the value of k is different for all pairs. This means that y does not vary directly with x.
