Linear Equations

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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Min X = Max X = Min Y = Max Y =

GeoGebra is a GNUed software package for mathematics visualization.  The home for the applications is  http://www.geogebra.org.

Return to the Calculus Applet page.
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Last updated By Mike May, S.J., October 12, 2007.