I'm trying to use a variable in a grep regex.  I'll just post an example of the failure and maybe someone can suggest how to make the variable be evaluated while running the grep command.  I've tried ${var} as well.
$ string="test this"
$ var="test"
$ echo $string | grep '^$var'
$ 
Since my regex should match lines which start with "test", it should print the line echoed thru it.
$ echo $string
test this
$