This page explores linear equations, linking the algebraic methods
with corresponding geometric interpretations.
To define a line, we typically need two pieces of information,
either a pair of points, or a point and a slope, or a slope and an
intercept. Each window below lets the user define a line using
one of these sets of information, and provides the transformation into
the other formats.
We start with the two point definition of a line. The points P
and Q are draggable. The applet window walks through the two
point definition of the line along with the transformation to the
point-slope format, the slope intercept format, and the general
equation
format.
The first window is set up with sliders for a, b, and c, in
the
quadratic equation y=a*x^2+b*x+c. The graph of the function is
also given.
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We next look at the point-slope definition of a line. The
point P is draggable and the slider value m controls the slope. The
second window is again set up to define produce the other three forms
of the linear equation. To make the computations easier we assume
that the second point is set up with a change in x of size 1, thus
having a change in y of size m.
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The third window starts with the slope intercept construction.
This
is a special case of the point slope construction, with the extra
condition that the point is on the y-axis. Since by convention
the intercept is traditionally b, we designate the point of the
intercept as B=(0,b). The values of b and m are both controlled
by sliders. As in the second window, we find the second point by
letting makingthe change in x of size 1, thus
having a change in y of size m.
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GeoGebra is a GNUed software package for mathematics visualization.
The home for the applications is http://www.geogebra.at.
Return to the Calculus
Applet page.
Return to the GeoGebra
Applet page.
Last updated By Mike May,
S.J., October 12, 2007.