Cook linguine according to the directions on the package in salted water.
In large skillet, melt the butter and olive oil over medium-low heat. Add the garlic. Saute for 1 minute. Be careful, the garlic burns easily! Add the shrimp, 1 1/2 teaspoons of salt, and the pepper and saute until the shrimp have just turned pink, about 5 minutes, stirring often. Remove from the heat, add the parsley, lemon zest, lemon juice, lemon slices, and red pepper flakes. Toss to combine.
When the pasta is done, drain the cooked linguine and then put it back in the pot. Immediately add the shrimp and sauce, toss well, and serve.