With a , the tax rate decreases as income individuals bear a greater burden with this type of tax.
1st blank a: direct, progressive, proportional, regressive .
2nd blank a: higher income , lower income

REGRESSIVE ... lower income

So the full sentence would read:  With a regressive, the tax rate decreases as income increases. Lower income individuals bear a greater burden with this type of tax.

An example of a regressive tax would be a sales tax on everyday items.  Lower income individuals must spent a higher percentage of their income on basic necessities, so sales taxes on necessary items takes from them a higher percentage of their income than is the case for wealthy individuals.  If there are higher rates of tax on luxury items (like yachts or luxury cars) that are purchased only by higher-income people, that would not be regressive. But otherwise sales taxes affect a greater percentage of the poor's income than the rich.

Another example (and another consumption tax) would be taxes on gasoline.  Think of two commuters who both drive 30 miles a day to get to work, in cars that get similar gas mileage.  If one of those persons makes $100,000 a year, and the other person has a job that earns only $25,000 a year, the person earning $25,000 a year is paying the same amount in gas taxes as the person making $100,000 a year.  That's a regressive tax.  
[A detail to note:  Americans on average across the country pay about 50 cents in taxes that is included in the price of each gallon of gas purchased.]