Equations of a line

Symmetry 50. Intercepts 50. Asymptotes 50. Equations of Slope 51. Tangents 51. Equations of a Straight Line 52. Equations of a Circle 53. Equations of a Parabola 53. Equations of an Ellipse of Eccentricity e 54. Equations of a Hyperbola 55. Equations of Three-Dimensional Coordinate Systems 56. Equations of a Plane 56. Equations of a Line 57. Equations of Angles 57. Equation of a Sphere 57. Equation of an Ellipsoid 57. Equations of Hyperboloids and Paraboloids 58. Equation of an Elliptic Cone 59. Equation of an Elliptic Cylinder 59. 

Equation (1.3) follows readily from the point-slope equation of a line, applied to the tangent at (ay, /(x )), namely to... 

The above equation can be rearranged into the equation of a line ... 

Equation 8.7 is the equation of a line passing through the origin (zero intercept) with x plotted on the ordinate and 1 /T plotted on the abscissa. The slope of the line is C, the Curie constant. Equivalently, a plot of 1 /x versus T yields a straight line with slope 1/C (Fig. 8.3b). For the case of classical mechanics, Paul Langevin (1872-1946) later showed that the exact form of the equation for the magnetic susceptibility, in fields insufficient to cause saturation, is ... 

Equations like these always have the form of the equation of a line (y = ax + b). If (°A) and (°B) stand for any two temperature units, to derive the equation for T(°B) in terms of T(°A) you must know equivalent values on each scale of two temperatures—say. Ti and Tz-Then... 

In three space, a line is defined as the intersection of two non-parallel planes, such as 2x + y + 4z = 0 and x + 3y + 2z = 0. Standard equations of a line in three space are the two-point form ... 

Find the equation of a line which will pass through the point (4, - 4) and whose tangent is 2. Ansr. y - 2x + 12 = 0. 

Since this class assumes students have not taken calculus, the tangent will be approximated by finding the equation of a line between two very close points, which are denoted (x) and (x + 5x). The method works as follows ... 

Let X s x(t) be the equation of a line of discontinuity. Then across it the Eankine-Hugoniot jump conditions hold. 

The following formulas are used to calculate the equation of a line, y= ax + b (Cohen and Cohen 1983, 41-43) ... 

Calculate the term a for the equation of a line using the using the methodology presented in this chapter. 

This is the point-slope equation of a line, where x is the base point and/(x ) is the slope [derivative affix) evaluated atx ]. Solving Equation 1.8 for x at which/(x) = 0 gives... 

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