There's not such a method in StreamReader class that reads a specific line, see StreamReader.ReadLine Method . Instead, if you need a specific line, read the lines to a string array and get the specific line from the array.
Another solution would be to use counter variable for the lines:
Dim path As String = Environment.GetFolderPath(Environment.SpecialFolder.ApplicationData)
Dim file As String = (path + "\LogDat.txt")
Dim sr As New IO.StreamReader(file)
Dim line1 As String
Dim line4 As String
Dim line9 As String
Dim thisLine As String
Dim lineCounter As Integer = 1
Do
thisLine = sr.ReadLine()
If thisLine IsNot Nothing Then
If lineCounter = 1 Then line1 = thisLine
If lineCounter = 4 Then line4 = thisLine
If lineCounter = 9 Then line9 = thisLine
End If
lineCounter += 1
Loop Until thisLine Is Nothing
sr.Close()
HTH