Dynamic Views for solving equality of two linear functions, \$f(x) = g(x)\$,
where \$f(x)= m_fx+b_f\$ and \$g(x)= m_gx+b_g \$ on Graphs and Mapping Diagrams
 For the graph of \$f\$ and \$g\$: Find the point at the intersection of the graphs of \$f\$ and \$g\$, \$(x_*,y_*)\$, determine it's first coordinate, \$x_*\$, and that is the desired value for \$x\$, and its second coordinate, \$y_*\$, is the desired value for \$y\$. For the mapping diagram of \$f\$ and \$g\$: Find the focus points of \$f\$, \$F= [m_f, b_f]\$, and \$g\$, \$G=[m_gb_g]\$, on the mapping diagram. Draw the line through \$F\$ and \$G\$, to find the point of intersection of this line with the X axis, \$x=x_*\$, which is the desired value for \$x\$ and the Y axis, \$y=y_*\$ for the desired value of \$y\$. Notice how the point on the graph is paired with the points and arrow on the mapping diagram.

• Enter expressions in the input boxes to change the functions \$f\$ or \$g\$.
• Check the box to see the focus points (when \$m \ne 1\$) and lines from the point \$x=0\$ on the mapping diagram.
• Check the box to see the solution of the equation visualized on the graph and the mapping diagram.

Martin Flashman, Aug. 11, 2018, Created with GeoGebra