Solution: Substitute X=3 into Y=2X- 1, Y = 2x3- 1 = 5, and the coordinate of the intersection of straight line L and straight line Y=2X- 1 is (3,5).

Substituting Y=-4 into Y=-X-2, we get, -4=-X-2, X=4-2=2, and the coordinate of the intersection of straight line L and straight line Y=-X-2 is (2, -4).

The straight line l passes through (3, 5); Two o'clock direction

Let the analytical formula of the straight line L be y=kx+b, and let x = 3 and y = 5； respectively; X=2, y=-4 and y=kx+b, there is an equation:

5=3k+b

-4=2k+b

Solution: k=9, b=-22.

Substitute k = 9 and b =-22 into y=kx+b, and the analytical formula of the straight line l is: y=9x-22.