Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9-inch round or square baking pan.
Add the sugar and butter to a large mixing bowl, and beat until the combination is light and fluffy, and a light yellow in color.
Continue to beat as you add the eggs and vanilla extract.
In a separate bowl, measure the flour, baking powder, baking soda, and salt, and sift to combine.
Add the dry ingredients to the butter mixture in three batches, alternating with the yogurt.
Add the lemon zest and juice last, and beat until smooth.
Pour into the prepared pan, and bake in the oven for about 35 minutes, until a knife inserted in the center comes out clean.
Cool for about 10 minutes and remove from pan.
Dust with powdered sugar and top with lemon slice, if desired.