Draw the budget line for a consumer who can consume two goods (X and Y). The price of X is $10, the price of Y is $20, and the consumer's income is $1000.

A consumer originally faces the budget line P_XX + P_YY = M. The price of good X doubles, the price of good Y quadruples, and income becomes 3 times larger. Write down an equation for the new budget line in terms of the original prices and income.

With the quantity of X plotted on the x-axis, if the price of good Y increases, but the price of good X remains unchanged, does the budget line become flatter or steeper? Draw a diagram illustrating your answer.