I guess the below should work (instead of the writer part from your example). I'm unfortunately with no build environment so It's from memory but I hope it helps
using (var fs = File.Open(filePath, FileMode.Open, FileAccess.ReadWrite)))
{
var destinationReader = StreamReader(fs);
var writer = StreamWriter(fs);
while ((line = reader.ReadLine()) != null)
{
if (line_number == line_to_edit)
{
writer.WriteLine(lineToWrite);
}
else
{
destinationReader .ReadLine();
}
line_number++;
}
}