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
- 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