The linear function $f$ determines a non-vertical line with its graph.

Similarly, as long as $m \ne 1$ , the linear function $f$ determines a specific point on the mapping diagram which we will call

Review of some of the previous examples. You will notice that the arrows in these examples where $m \ne 1$ meet at a common point- the focus point for that linear function, and when $m = 1$, the arrows and lines are all parallel.

You can use this next dynamic example to investigate the effects of the linear coefficient and the constant term simultaneously on the focus point in a mapping diagram of $f$ and the line in the graph of $f$.

Example LF.DFP.0 Dynamic Visualization of Focus Point for
Linear Functions: Graphs, and Mapping Diagrams

Note: The value of $m$ places the focus point by its distance from the two axes.

For a fixed vale of $m$ the value of $b$ places the focus on a line determined by $m$ parallel to the domain (source) axis.