A proposed merger between American Airlines and U.S. Airways has won Justice Department approval, paving the way for what would be the world’s largest airline. The airlines reached an agreement with federal regulators just two weeks before a scheduled trial. Under the deal, the two airlines would give up dozens of take-off and landing slots at several major airports to lower-cost carriers. The pact still needs approval from the Federal District Court in Washington, D.C., and the judge overseeing American’s bankruptcy case. If approved, more than 70 percent of the airline passenger business would fall under the control of four airlines.