If we know the intercepts and the slope of a linear equation, we know everything there is to know about it. Sure, we may not know where it was born, who its favorite musical artist is or its stance on marriage equality, but for our purposes, we know it well enough.
There are different ways to package this information. That is, the same linear equation can be written in multiple ways.
This fact shouldn't come as too much of a surprise, so wipe that "surprised face" off your mug. After all, we already know that equations can be rearranged to produce equivalent equations. The following equations are all equivalent to each other (check and see):
These equations are in the three most common forms used for writing linear equations:
For each of these forms, we'll talk about how to go from the equation to the graph, and how to go from the graph to the equation. It isn't simply a matter of hitting "Reverse Directions" on your GPS.