1. **State the problem:** We need to find the roof installation cost when the area of the roof is 144 square feet. 2. **Understand the relationship:** The graph shows a straight line from the origin (0,0) to (20,80), indicating a linear relationship between area and cost. 3. **Find the formula:** Since the line passes through the origin, the cost $C$ is proportional to the area $A$. The formula is: $$C = kA$$ where $k$ is the constant of proportionality (cost per square foot). 4. **Calculate $k$ using the given point (20, 80):** $$k = \frac{C}{A} = \frac{80}{20} = 4$$ So, the cost per square foot is 4. 5. **Calculate the cost for 144 square feet:** $$C = 4 \times 144 = 576$$ 6. **Final answer:** The roof installation cost for 144 square feet is **576**.