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

The number $m$ is referred to as the "slope" and the value of $f(0) = b$ gives the second coordinate of the Y-intercept, $(0,b)$ for the graph of $f$

There are one other very useful form for the linear function $f$ that uses $m$, the slope of $f$, and the value of $f$ at any input. This form is called the "point -slope" form of $f$.

If we assume the slope of $f$ is $m$ and $f(x_0) = y_0$, then the point $(x_0,y_0)$ will be on the graph of $f$ and one can find $f(x)$ by using the equation

$f(x) = y_0 + m(x-x_0)$.

Expanding the last equation gives $f(x) = y_0 +mx -mx_0 = mx + (y_0
-mx_0) = mx +b$ where $ b = y_0 -mx_0$.These two forms, as well as how to find the value of $m$ from two values for $f$, 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.

To be added... A dynamic example to visualize finding $m$ and the point slope form of a linear function with a mapping diagram of $f$ and the lines in the graph of $f$.