1. **State the problem:** Layla's gas tank capacity is 10 gallons. After driving for 4 hours, 5 gallons remain. We need to write an equation for $G$ (gallons remaining) in terms of $t$ (hours driven). 2. **Identify the type of problem:** This is a linear relationship because gas is used at a constant rate over time. 3. **Find the rate of gas consumption:** Initial gas = 10 gallons Gas after 4 hours = 5 gallons Gas used in 4 hours = $10 - 5 = 5$ gallons Rate of consumption = $\frac{5 \text{ gallons}}{4 \text{ hours}} = \frac{5}{4}$ gallons per hour 4. **Write the linear equation:** The amount of gas remaining decreases by $\frac{5}{4}$ gallons every hour. So, the equation is: $$G = 10 - \frac{5}{4}t$$ where $G$ is gallons remaining and $t$ is hours driven. 5. **Explain:** - At $t=0$, $G=10$ gallons (full tank). - For each hour driven, subtract $\frac{5}{4}$ gallons from the tank. This equation models the gas remaining after $t$ hours of driving. **Final answer:** $$G = 10 - \frac{5}{4}t$$