Equation for a line in R2 | two points.

 


Example 1, equation of a straight line in form of ax + by + c = 0 is,

x - y + 0 = 0. Thus ( a = 1, b= - 1, c=0).

direction vector of line is (-b, a) = (1, 1).

line passing through point, (0, -0/1) = (0,0)

 =  (1,1)

Parametric form of the line passing through (x0,y0) with direction vector of (1,1)
x = xa + t d
y = ya + t d

For R3 parametric form is, 
thus, direction vector, can be defined in terms of angle.
alternatively, given angle with x line and passing through point, we can calculate equation for line.

Thus, equation of the line with angle of 45 degrees is,
x - y = c, and value of c can be from +/- infinity.

slope for above line is 1, with constant 0,
indicates y=x and line passing through origin.
line for the line: x-y =0.

line for the line: y = x + 2
when x is zero, y=2.

line for the line: y = x - 2
when x is zero, y is -2.




Reference










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