1. **Problem statement:** A person has 120 to spend on two goods X and Y with prices 3 and 5 respectively. 2. **Budget line formula:** The budget line equation is given by $$3X + 5Y = 120$$ where $X$ and $Y$ are quantities of goods. 3. **Original budget line:** To find intercepts: - When $Y=0$, $3X=120 \Rightarrow X=\frac{120}{3}=40$ - When $X=0$, $5Y=120 \Rightarrow Y=\frac{120}{5}=24$ So the original budget line intercepts are $(40,0)$ and $(0,24)$. 4. **Case A: Draw original budget line** - The line connects points $(40,0)$ and $(0,24)$. 5. **Case B: Budget falls by 25%** - New budget = $120 - 0.25 \times 120 = 90$ - New budget line: $$3X + 5Y = 90$$ - Intercepts: - $X=\frac{90}{3}=30$ - $Y=\frac{90}{5}=18$ 6. **Case C: Price of X doubles** - New price of X = $3 \times 2 = 6$ - Budget remains 120 - New budget line: $$6X + 5Y = 120$$ - Intercepts: - $X=\frac{120}{6}=20$ - $Y=\frac{120}{5}=24$ 7. **Case D: Price of Y falls to 4** - New price of Y = 4 - Budget remains 120 - New budget line: $$3X + 4Y = 120$$ - Intercepts: - $X=\frac{120}{3}=40$ - $Y=\frac{120}{4}=30$ **Summary of intercepts:** - Original: $(40,0)$ and $(0,24)$ - Budget down 25%: $(30,0)$ and $(0,18)$ - Price of X doubles: $(20,0)$ and $(0,24)$ - Price of Y falls to 4: $(40,0)$ and $(0,30)$ These lines can be graphed by plotting the intercepts and connecting them with straight lines.