Q.Find the equation of the line passing through the point of intersection of lines x + 2y − 6 = 0 and 2x − 3y + 4 = 0 and making intercept 3 on the X-axis.

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 thr …