The point at which you turn a bar chart or scatterplot into a line chart is when and only when intermediary values can be linearly interpolated between adjacent values.
This is often the case when the X axis is time, but far from always, and there are other types of X axis that satisfies that property too.
That's the strict way of looking at it.
Slightly more loosely speaking, a line also helps comparing whether adjacent values are higher or lower, because humans are fairly good at judging angles relative to each other. So under this looser requirement, the X axis values have to be such that adjacent ones are more comparable than further apart ones.
Under the looser requirement, time is actually a surprisingly bad X axis because values further apart are normally just as valid comparisons as those close together!
There's a third, very loose reason to connect the points of a scatterplot with lines: it helps the eye judge the sequence of points, and thus get a sense of the internal variation in the series.
This is a very loose requirement, but also a powerful tool.
This is often the case when the X axis is time, but far from always, and there are other types of X axis that satisfies that property too.
That's the strict way of looking at it.
Slightly more loosely speaking, a line also helps comparing whether adjacent values are higher or lower, because humans are fairly good at judging angles relative to each other. So under this looser requirement, the X axis values have to be such that adjacent ones are more comparable than further apart ones.
Under the looser requirement, time is actually a surprisingly bad X axis because values further apart are normally just as valid comparisons as those close together!
There's a third, very loose reason to connect the points of a scatterplot with lines: it helps the eye judge the sequence of points, and thus get a sense of the internal variation in the series.
This is a very loose requirement, but also a powerful tool.