1. **State the problem:** We are given the cost of hiring a surfboard which includes an up-front fee plus an hourly rate. The cost for 3 hours is 50 and for 7 hours is 90. We need to find the cost rule $C$ in terms of time $t$, the cost per hour, and the up-front fee. 2. **Identify the formula:** The cost $C$ can be modeled as a linear function of time $t$: $$C = mt + b$$ where $m$ is the hourly rate (slope) and $b$ is the up-front fee (y-intercept). 3. **Use the given points:** We have two points $(3, 50)$ and $(7, 90)$. 4. **Calculate the slope $m$ (cost per hour):** $$m = \frac{90 - 50}{7 - 3} = \frac{40}{4} = 10$$ 5. **Find the up-front fee $b$:** Use one point and the slope in the equation $C = mt + b$. Using $(3, 50)$: $$50 = 10 \times 3 + b$$ $$50 = 30 + b$$ $$b = 50 - 30 = 20$$ 6. **Write the cost rule:** $$C = 10t + 20$$ 7. **Interpret the results:** - The cost per hour is $10$. - The up-front fee is $20$. **Summary:** - The graph is a straight line passing through points $(3, 50)$ and $(7, 90)$ with slope $10$ and y-intercept $20$.