Plotting a graph takes time. Often mathematicians just want to know the key features. These are: shape, location and some key points (such as where the graph crosses the axes or turning points).

If an equation can be rearranged into the form \(y = mx + c\), then its graph will be a straight line. In the above: \(x + y = 3\) can be rearranged as \(y = 3 - x\) (which can be re-written as \(y = ...