1. **Stating the problem:** We have the linear function $y = 36.9x$ which represents the relationship between gallons of gas ($x$) and miles driven ($y$). 2. **Formula and explanation:** This is a linear equation in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Here, $m = 36.9$ and $b = 0$. 3. **Interpretation:** The slope $36.9$ means for every 1 gallon of gas, the car can drive 36.9 miles. 4. **Graph features:** Since $b=0$, the line passes through the origin (0,0). The slope is positive, so the line rises from left to right. 5. **Summary:** The function $y = 36.9x$ models a direct proportionality between gallons of gas and miles driven, with no fixed starting miles. **Final answer:** The linear function is $y = 36.9x$, passing through the origin with slope 36.9.