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

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