[RESOLVED] Getting rid of lines drawn under other lines

[DinosaurusRex]

I'm trying to copy that microsoft screen saver with the moving line on a black background, and I've reached a barrier.
Perhaps it's just best you look at my code before I try to explain myself, it could get confusing.

Public Class Form1

    Private Sub Form1_Load(sender As Object, e As EventArgs) Handles MyBase.Load
        Randomize()
        g = Me.CreateGraphics

        While y1c = y2c
            y1c = 3 + CInt(7 * Rnd()) 'makes endpoint location change values different
        End While

        While x1c = x2c
            x1c = 3 + CInt(7 * Rnd())
        End While

        Me.BackColor = Color.Black

        Timer.Start()

    End Sub

    Dim i1 As Integer = CInt(255 * Rnd()) 'argb values
    Dim i2 As Integer = CInt(255 * Rnd())
    Dim i3 As Integer = CInt(255 * Rnd())

    Dim g As Graphics

    Dim x1 As Integer = CInt(Rnd(Me.Width)) 'line endpoint location values
    Dim y1 As Integer = CInt(Rnd(Me.Height))
    Dim x2 As Integer = CInt(Rnd(Me.Width))
    Dim y2 As Integer = CInt(Rnd(Me.Height))

    Dim x1c As Integer = 3 + CInt(7 * Rnd()) 'line endpoint location change values
    Dim y1c As Integer = 3 + CInt(7 * Rnd())
    Dim x2c As Integer = 3 + CInt(7 * Rnd())
    Dim y2c As Integer = 3 + CInt(7 * Rnd())

    Private Sub Timer_Tick(sender As Object, e As EventArgs) Handles Timer.Tick

        i1 = i1 + 1
        i2 = i2 + 2
        i3 = i3 + 3
        If i1 > 255 Then i1 = 1
        If i2 > 254 Then i2 = 1
        If i3 > 253 Then i3 = 1

        x1 = x1 + x1c
        If x1 > Me.Width Or x1 < 0 Then x1c = x1c * -1
        y1 = y1 + y1c
        If y1 > Me.Height Or y1 < 0 Then y1c = y1c * -1

        x2 = x2 + x2c
        If x2 > Me.Width Or x2 < 0 Then x2c = x2c * -1
        y2 = y2 + y2c
        If y2 > Me.Height Or y2 < 0 Then y2c = y2c * -1

        g.DrawLine(New Pen(Color.FromArgb(i1, i2, i3), 1), New Point(x1, y1), New Point(x2, y2))

    End Sub
End Class

I just need help with getting rid of the lines that it has drawn after ~15 lines have been drawn after those *EFFICIENTLY*, so the screen doesn't feel so cluttered after a moment of it running.
Thanks!