Extended extension of the extension, lets you initialize line number:
https://gist.github.com/AndrewR66/1aab13658e2a48586760a054e6b6beea

Great start, Mark Hurd,

I have a simple extension of your extension:

static class extensionMeth
{
static int offset=0;
public static T DumpLine<T>(this T obj, string description = "", [CallerLineNumber]int lineNumber = 0)
{
if (offset == 0)
offset = lineNumber-1;

return obj.Dump($"Line:{lineNumber-offset}, {description}");
}
}

// Usage:
void Main()
{
"TestA".DumpLine("foo");

"TestB".DumpLine("bar");
"TestC".DumpLine();
}

Output, first DumpLine command gets line number 1:
Line:1, foo
TestA
Line:3, bar
TestB
Line:4,
TestC

If @Joe was interested in interleaving #line (C#) and #ExternalSource (VB) directives into the backend code, you could simply use the CallerLineNumberAttribute https://msdn.microsoft.com/en-us/library/system.runtime.compilerservices.callerlinenumberattribute.aspx in your own DumpLine extension method:

public static T DumpLine<T>(this T obj, string description, [CallerLineNumber]int lineNumber = 0)
{
return obj.Dump($"{description} Line:{lineNumber}");
}

That works, as is, except the line numbers include 33 (C#) or 28 (VB) preliminary lines for statements mode (presumably depending upon the number of Namespaces included).

You could also use the Dump(string description) overload:

var name = "Casey Chester";
name.Dump("Name");

Output:

Name

Casey Chester