Find the equation of a straight line passing through the intersection of 2x + 5y - 4 = 0 with x-axis and parallel to the line 3x - 7y + 8 = 0.

The equation of a line is 3x + 4y - 7 = 0. Find

(i) slope of the line.

(ii) the equation of a line perpendicular to the given line and passing through the intersection of the lines x - y + 2 = 0 and 3x + y - 10 = 0.

Prove that the line through (0, 0) and (2, 3) is parallel to the line through (2, -2) and (6, 4).

Prove that the line through, (-2, 6) and (4, 8) is perpendicular to the line through (8, 12) and (4, 24).