Q.Find the slope, X-intercept, Y-intercept of the line 2x + 3y − 6 = 0.

Every line, whatever information originally defined it, can be written as ax + by + c = 0 — the general form. From the coefficients alone you can read off the line's slope as −a/b (when b ≠ 0), its X-intercept as −c/a (when a ≠ 0), and its Y-intercept as −c/b (when b ≠ 0); a = 0 signals a line parallel to the X-axis (no X-intercept), and b = 0 signals a line parallel to the Y-axis (no Y-intercept). Two lines a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 are parallel exactly when their slopes −a1/b1 and −a2/b2 are equal (equivalently a1/a2 = b1/b2), and are identical (the same line) exactly when all three ratios a1/a2, b1/b2, c1/c2 agree. The general form is the common currency the chapter converts every other form into whenever a computation — reading a slope, checking parallelism or perpendicularity, or applying a distance formula — needs it in that shape.