The elongated 787-9 variant of Boeing Company’s Dreamliner made its first flight Tuesday, passing a key milestone for a model that should be more profitable both for the aerospace giant to sell and for its commercial customers to operate. The 787-9 took off Tuesday morning from Paine Field, near the Everett, Washington state factory where the jetliner was assembled. The extended model has room for 290 passengers, 40 more than the current production model, and has about 480 more kilometers of range, meaning Boeing can charge more for the airplane and airlines can sell more seats on longer flights. Boeing spokeswoman Kate Bergmann said the 787-9 has 388 firm orders, which account for 40 percent of all Dreamliner orders. After flight tests and certification, the first 787-9 will be delivered next June to the first customer, Air New Zealand.