Casper consumes goods x and y. Good x is sold at a price of P_x = $4 per unit. Good y is sold at a price of P_y = $1 per unit. Casper's income is m = $20 and his utility function is U(x, y) = 3x + y. (10 pts total)

1. Draw Casper's budget line. Find the slope of the budget line. (2pts)
2. Draw the indifference curve for utility level U(x, y) = 15. Sketch a couple more indifference curves. Pay attention to the shape of the indifference curves. (2 pts)
3. Find the amount of each good Casper demands at the optimal choice given the prices and income. Explain your answer. (4pts)
4. Given the price of Good y at $1 per unit, for what prices of x will Casper change his demand? (2pts)