Advanced MySql Query: Update table with info from another table

I would like to update a table in mySql with data from another table.

I have two tables "people" and "business". The people table is linked to the business table by a column called "business_id".

The necessary table structure, primary key is starred (Table: columns): People: *business_id, *sort_order, email Business: *business_id, email

I would like to update the business table email column with the email from the people table, something like this (I know I am missing something here):

UPDATE business b SET email = (SELECT email  from People p where p.business_id = b.business_id AND sort_order = '1') WHERE b.email = ''; 

Does this make sense? Is it possible?

UPDATE business b, people p
   SET b.email = p.email
 WHERE b.business_id = p.business_id
   AND p.sort_order = '1'
   AND b.email = ''

Note, if sort_order is an INT, then don't use '1' - use 1:

UPDATE business b
JOIN People p
ON p.business_id = b.business_id
AND p.sort_order = '1'
SET b.email = p.email
WHERE b.email = '';