What is the difference between a negatively and positively sloped income-consumption curve?

How do you derive that the slope of a budget line is -p1/p2? I'd like to see the mathematical process. Thanks!

Simone likes peanut butter and jelly (PB&J) sandwiches. When Simone makes a PB&J sandwich she always uses 4 tablespoons of peanut butter and 2 tablespoons of jelly. Suppose that the price of peanut butter is $0.05 per tablespoon and that the price of jelly is $0.15 per tablespoon. Simone lives above a bakery and receives free day old bread from her baker friend. The amount of Simone's income spent on PB&J sandwiches is $8 a week. Which of the following statements is true? A. Simone's indifference curves for peanut butter and jelly are normal indifference curves. B. Simone's indifference curves for peanut butter and jelly are straight lines, since she always eats peanut butter and jelly in a particular combination. C. Simone's indifference curves for peanut butter and jelly each have a right angle, since peanut butter and jelly are perfect complements for Simone. D. Simone maximizes her utility from PB&J sandwiches by consuming 8 sandwiches a we O E. Answers (C) and (D) are both true.

Consider the diagram below showing a consumer's choice of goods (Trainers and Electricity), following a rise in the price of Trainers. Identify which statement about the diagram is true. Electricity BL3 BLZ C B IC3 X3 X₂ A X₁ IC₂ -IC₁ BL₁ Trainers O The original consumption bundle is given by point C; the new consumption bundle is given by point A; BL3 represents the compensated budget line, using the Slutsky substitution effect; Trainers are a Giffen good. The original consumption bundle is given by point C; the new consumption bundle is given by point A; BL3 represents the compensated budget line, using the Slutsky substitution effect; Trainers are a normal good. The original consumption bundle is given by point A; the new consumption bundle is given by point C; BL3 represents the compensated budget line, using the Hicksian substitution effect; Trainers are a Giffen good. The original consumption bundle is given by point A; the new consumption bundle is given by point C; BL3…