Using a line graph
Only use lines to connect data points together if the data points are connected to one another. This typically means change over time.
For example, the price of a pear in 1996 and 1997 are related, so you can draw a line between those two data points. The price of a pear and the price of a grape are not related, so you cannot draw a line between those two data points.
Read more/see an exampleSmoothing out jagged lines
If you're graphing something over time and the lines are jumping up and down a lot, you should try resampling the data into a larger timeframe. No one can read a jagged line, and if they can they don't enjoy doing it!
For example, let's say I'm graphing the money I spend on groceries every day. Since I don't grocery shop every day, the line is going to be very very erratic - usually $0, but sometimes it will jump up to $20 or even $150. If I graphed my grocery spending on a weekly or monthly basis, though, it would even the line out.
Even though the original daily graph had more raw information, the way it was presented made the graph less informative.