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  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 equation of a line when two points are given – GeoGebra Lesson Explainer: Equation of a Straight Line in Space: Parametric Form | Nagwa Positi