Does line plots display individual data?

Answer 1

They can do, but there are some circumstances where they may not be particularly useful.

If, for example, the observations are not in order of the values of the independent variable, then a line plot will be difficult to read. If there are several different values of the dependent variable for a single value of the independent variable, the graph may be difficult to interpret. If there are two or more observations where the values of both variables are the same, the graph may not indicate that the point is in fact a multiple observation.