Final answer:
Yes, the relationship is a direct variation relationship.
Step-by-step explanation:
The graph of a relationship passes through the points (2,15.5) and (3,97). When this data is graphed, the result is a straight line, indicative of a direct relationship. In a direct variation relationship, as one variable increases, the other variable also increases in a proportional manner.
The equation of a direct variation relationship is in the form y = kx, where y and x represent the dependent and independent variables respectively, and k is the constant of variation.
In this case, we can find the constant of variation by substituting one of the points into the equation:
15.5 = k(2)
k = 7.75
Therefore, the equation for this direct variation relationship is y = 7.75x.