## The effect of the sign of the slope in y = ax

A linear function is a function whose equation is of the form $y = ax + b$. We separate the discussion about it into two parts: $b = 0$ and $b \neq 0$. In this post, we only discuss the graph of $y = ax + b$ where $b = 0$. We discuss the effect of the sign of the slope in $y = ax$.

If we let $b = 0$, the equation $y = ax + b$ becomes $y = ax + 0$ or simply $y = ax$.

Notice that if $x = 0$, then $y = ax = a(0) = 0$. This means that the graph contains the point with coordinates $(0,0)$. Therefore, $y = ax$ passes through the origin.

Generalization 1: The graph $y = ax$ passes through the origin.

We now examine the effect of the values of $a$. There are three cases: $a = 0$, $a > 0$, and $a < 0$» Read more