A linear function is a function whose equation is of the form . We separate the discussion about it into two parts: and . In this post, we only discuss the graph of where . We discuss the effect of the sign of the slope in .
If we let , the equation becomes or simply .
Notice that if , then . This means that the graph contains the point with coordinates . Therefore, passes through the origin.
Generalization 1: The graph passes through the origin.
We now examine the effect of the values of . There are three cases: , , and . » Read more