rough two pointsThe LINE through two distinct points (x1, y1) and (x2, y2) is given by(1) y = y1 + [(y2 - y1) / (x2 - x1)]·(x - x1),where x1 and x2 are assumed to be different. In case they are equal, the equation is simplified tox = x1and does not require a second point.Equation (1) can also be written asy - y1 = [(y2 - y1) / (x2 - x1)]·(x - x1),or even as(x2 - x1)·(y - y1) = (y2 - y1)·(x - x1),where one does not have to WORRY whether x1 = x2 or not. However, the SIMPLEST for me to remember is this(y - y1)/(y2 - y1) = (x - x1)/(x2 - x1)which is not as universal is the one before.General equationA straight line is defined by a linear equation whose general form isAx + By + C = 0,where A, B are not both 0.The coefficients A and B in the general equation are the components of vector n = (A, B) normal to the line. The pair r = (x, y) can be looked at in two ways: as a point or as a radius-vector joining the origin to that point. The latter interpretation shows that a straight line is the locus of points r with the propertyr·n = const.That is a straight line is a locus of points whose radius-vector has a fixed scalar PRODUCT with a given vector n, normal to the line. To see why the line is normal to n, take two distinct but otherwise arbitrary points r1 and r2 on the line, so thatr1·n = r2·n.But then we conclude that(r1 - r2)·n = 0.In other words the vector r1 - r2 that joins the two points and thus lies on the line is perpendicular to n