Shapes of Budget Constraints - One Price Negative
Commodity 1 is stinky garbage. You are paid $2 per unit to accept it; i.e. p1 = - $2. p2 = $1. Income, other than from accepting commodity 1, is m = $10.
Then the constraint is - 2x1 + x2 = 10 or x2 = 2x1 + 10.