solving Linear Equations Dynamic Mapping Diagrams and Graphs

Dynamic Views for solving an equation $f(x) = mx+b = c$ on Graphs and Mapping Diagrams

For the graph of $f$: Find $y=c$ on the Y axis, then find the point on the graph of $f$ directly right (left) of that point, $(x_*,c)$, determine it's first coordinate, $x_*$, and that is the desired value for $x$.

For the mapping diagram of $f$: Find $y=c$ on the Y axis , then find the focus point of $f$, $F= [m, b]$ on the mapping diagram. Draw the line through F and the point $y=b$, to find the point of intersection of this line with the X axis, $x=x_*$, which is the desired value for $x$.

Notice how the point on the graph is paired with the points and arrow on the mapping diagram.
Move the slider to change the value of $m$ or $b$.
Move the slider or enter a number in the box for the value of $c$ in the equation.
Check the box to see the focus point (when $m \ne 1$) and two lines from the point showing the relation to the mapping diagram.
Check the box to see the solution of the equation visualized on the graph and the mapping diagram.
Select the point $x$ in the mapping diagram to move the point by mouse to verify the solution.

Martin Flashman, Oct.21, 2013, Created with GeoGebra