How can you determine if a relationship is a direct variation using values from the table?
Varies Directly? Yes Constant of Proportionality: 0.2
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.
Price, x
Tax, y
y/x
k
20
4
4/20
0.2
25
5
5/25
0.2
30
6
6/30
0.2
35
7
7/35
0.2
Notice that the value of k for all pairs is 0.2. This means that y does vary directly with x, and the constant of proportionality equals 0.2.
