The Straight Line

In this page three forms of the equation of a straight line are presented. These examples make use mainly of the tools EQUATIONS and SEGMENTS of the nippe Descartes.

Every linear equation in x and y represents a straight line. There are three so called canonical equations for straight lines:

1. y=m*x+b

where m is the slope and b is the ordinate at the origin.

2. A*x+B*y=C

where a=C/A is the abscissa at the origin and b=C/B is the ordinate at the origin.

3. x/a+y/b=1

is called the normal form of the equation of a straight line.

There is another interesting equation for the straight line which is related to the normal form:

4. x*cos(pi*t)+y*sen(pi*t)=d

where pi*t is the angle formed by the normal or perpendicular to the line with respect to the x axis, and d is the distance to the origin.

In the four examples on this page Descartes uses three different ways to draw the graphsof the EQUATIONS. In the first example the straight line is represented as the graph of a function, or more precisely, as the graph of the equation  y=f(x) where the function f is defined by f(x)=m*x+b. In this case Descartes evaluates the function f(x) at all the values of x corresponding to the pixels on the screen inside the applet window and draws straight lines joining the consecutive points (x,f(x)) . In the second example Descartes takes advantage of its capacity to recognize some explicit equations like A*x+B*y=C and draws the straight line that passes through (0,B/C) and (C/A,0). Finally, in the examples 3 and 4 Descartes solves the equation in  x and y using an adaptation of Newton's method to find the zeroes of a function. In these two particular cases the "zero curves" turn out to be straight lines.

Introduction  Appetizer  Examples  Documentation  Applications  Work plan

	Ministerio de Educación, Cultura y Deporte. Aņo 2000