This form for a linear function is usually described as the "slope, Y-intercept" form of $l$.

The number $m$ is referred to as the "slope" and the value of $l(0) = b$ gives the second coordinate of the Y-intercept, $(0,b)$ for the graph of $l$In this form, $l$ is evaluated by $l(x) = m(x-x_0) +y_0 $.

This form is called the "point slope" form of $l$. The
value $l(x_0) = y_0$ gives the correspondence of the pair $(x_0,y_0)$ as
being a point on the graph of $l$ and the arrow $<x_0,y_0>$ as an arrow on the mapping diagram of $l$.

Expanding the point slope form equation gives $l(x) = m(x-x_0) +y_0 = mx - mx_0 +y_0$.

From this expression we can see the connection between $b$, $m$, and the pair $(x_0,y_0)$, namely, $b = y_0 - mx_0$.

These two forms are covered thoroughly in most algebra texts.

In this subsection we explore how mapping diagrams for linear functions help visualize these forms and the interpretation of $m$ as a magnification factor and a rate.

These help in understanding further the meaning of the X- and Y- Intercepts of the graph of $f$ through using mapping diagrams.