On a line graph, a line connects points representing data, showing the linear relationship of the data. On a scatter plot, the points are literally scattered on the graph, each representing a piece of data that is not necessarily related to the other data points. Use a line graph to show the connection among a set of interdependent numbers and a scatter plot to show correlation between two data sets that aren't necessarily related.
Line Graph

Your cat has just had a litter of kittens, and you want to see how quickly a particular kitten grows by weighing her on a scale each week. In week one, she weighs .52 pounds, week two .58 pounds, and so on, for 20 weeks, giving you a set of data that looks like [1, .52], [2, .58] and so on. Time is the independent variable, or x axis, and weight is the dependent variable, or y axis. On a line graph, plot these coordinates and draw lines between them.
Scatter Graph

Suppose you choose instead to weigh all the kittens at various times and intervals over the 20week period. Now you have many data points, and plotting them gives a collection of data points that may be scattered all over the graph. As with the line graph, the independent variable is time and the dependent variable is weight. You can't connect these points with a line, but you can see trends in the overall data, if a trend exists, by constructing a “bestfit” line through the clustered data.
Differences

Use line graphs to plot trends in a single data type, such as the weight of one kitten, and scatter plots to represent any data set representing a correlation. Construct a bestfit line through this data to estimate the trends and approximate the relationship between the dependent and independent variables.
References
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