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I would not say it is "needed," but basically the more points you have the better you can understand the graph. And three because its the recommmended minimum to get a gist of the graph, yet it will not take a lot of effort to plug in three numbers.

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Q: Why is a third point needed to graph an equation?
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How you can obtain the solution to a system of equations by graphing?

In the same coordinate space, i.e. on the same set of axes: -- Graph the first equation. -- Graph the second equation. -- Graph the third equation. . . -- Rinse and repeat for each equation in the system. -- Visually examine the graphs to find the points (2-dimension graph) or lines (3-dimension graph) where all of the individual graphs intersect. Since those points or lines lie on the graph of each individual graph, they are the solution to the entire system of equations.


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Why is it a good idea to locate 3 points when you graph an equation?

In theory you only need 2 since 2 points in the plane determine a line. However, we all make mistakes ( I make plenty!) and making sure that third point falls on the line you found from the other two is a good way to check for errors.