It all depends on the data. If you have an equation this can be easier because say example the equation is for concentration, c=n/v, where we are keeping n constant and changing v, resulting in a change in c. You can see that c is inversely proportional to v and this resembles a y=1/x hyperbola type of graph (a curve), while in a different equation that might be a line graph.
If the data is just random like from an experiment, then to decide between a line of best fit and a curve of best fit, just use common sense. If the relationship between the two axis looks curved it is probably a curve of best fit, likewise for line of best it, as I doubt the HSC examiners are going to make it vague as to what the relationship looks like