There are seven standard forms for the equation of a straight line. The slope-intercept form y = mx + c directly reveals the slope and y-intercept. The point-slope form y - y1 = m(x - x1) is used when a point and slope are known. The two-point form eliminates explicit slope calculation. The intercept form x/a + y/b = 1 is ideal when axis intercepts are given. The normal form x cos(alpha) + y sin(alpha) = p uses the perpendicular from the origin. The general form ax + by + c = 0 is the universal representation used in distance formulas. The parametric form x = x1 + r cos(theta), y = y1 + r sin(theta) is powerful for problems involving distances along a line. Choosing the right form based on given information is the key strategic decision. For instance, if intercepts are given, use intercept form. If a point and perpendicularity condition exist, use point-slope form with the negative reciprocal slope. Converting between forms is straightforward: from general form, slope = -a/b, x-intercept = -c/a, y-intercept = -c/b.