How can you determine if a relationship is a direct variation using values from the table?
Varies Directly? Yes Constant of Proportionality: 36
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.
Hours, x
Miles, y
y/x
k
3
108
108/3
36
5
180
180/5
36
7
252
252/7
36
9
324
324/9
36
Notice that the value of k for all pairs is 36. This means that y does vary directly with x, and the constant of proportionality equals 36.
