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