Analytical geometry straight line

Coordinate Systems The basic concept of analytic geometry is the establishment of a one-to-one correspondence between the points of the plane and number pairs (x, y). This correspondence may be done in a number of ways. The rectangular or cartesian coordinate system consists of two straight lines intersecting at right angles (Fig. 3-12). A point is designated by (x, y), where x (the abscissa) is the distance of the point from the y axis measured parallel to the x axis,... 

The previons equation is a straight-line equation between Int and InF. The equation is that of a straight line, so only two data points for Int and InF are required to calculate the constants m and K. Using the techniques of analytic geometry as applied to straight-line equations, the following equations are produced... 

Using the techniques of analytic geometry, let us derive the Freundlich constants in a little more detail than used in the derivation of the constants in the discussion of reverse osmosis treated previously. As mentioned, the straight-line form of the equation requires only two experimental data points however, experiments are normally conducted to produce not just two pair of values but more. Thus, the experimental resnlts must be reduced to just the two pairs of values required for the determination of the parameters therefore, assuming there are m pairs of values, these m pairs must be reduced to just two pairs. Once the reduction to two pairs has been done, the isotherm equation may be then be written to just the two pairs of derived values as follows ... 

Analytical Geometry of Straight lines and Plane Curves... 

The method of reversible distillation trajectories calculation is described above in Section 4.4. To determine coefficients of linear equations, describing straight lines, planes, and hyperplanes, going trough stationary points, by coordinates of these points well-known formulas of analytic geometry are used. 

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