An easy way to do this is to use variables in your DrawLine routine, and increment these variables every time you loop through your code. Here's a rudimentary example:
Graphics 800,600,0
Local i:Float, speed:Float
i# = 0
speed# = 5.0 ' increase this to speed the lines up; decrease to slow them down.
While Not KeyHit(Key_escape)
Cls
SetColor 0,160,0 ' change color to green
DrawRect 0,250,800,100 ' draw green box
SetColor 255,255,255 ' change color to white
DrawLine 0,250,i#,250 ' draw white line
DrawLine 0,350,i#,350 ' draw white line no. 2
Flip
i# = i# + speed#
If i# > 800 Then
i# = 800
EndIf
Wend
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