Final answer:
The direct variation equation that shows the relationship between x and y is y = 7x.
Step-by-step explanation:
A direct variation equation shows a linear relationship between two variables, where a change in one variable leads to a proportional change in the other.
In this case, let's represent the relationship between x and y.
We know that y = 14 when x = 2.
To write the direct variation equation, we can use the form y = kx, where k is the proportionality constant.
Substituting the known values, we have 14 = k(2). Solving for k, we find that k = 7.
Therefore, the direct variation equation that shows the relationship between x and y is y = 7x.