How can you determine if a relationship is a direct variation using values from the table?
Varies Directly? Yes Constant of Proportionality: 2.5
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.
Year, x
Height, y
y/x
k
5
12.5
12.5/5
2.5
10
25
25/10
2.5
15
37.5
37.5/15
2.5
20
50
50/20
2.5
Notice that the value of k for all pairs is 2.5. This means that y does vary directly with x, and the constant of proportionality equals 2.5.
