To determine the graph that represents the relationship between the distance driven ($D$) and gas used ($G$), analyze the proportional relationship indicated by the given points on each option's graph.

Step-by-Step Analysis:

1. The graph represents a linear relationship $D = mG$, where:

   • $m$ is the slope (distance per gallon of gas).

2. For each graph option, calculate the slope $m$:

   • Option A: Passes through (20, 200).
     Slope $m = \frac{\text{Distance}}{\text{Gas}} = \frac{200}{20} = 10 \, \text{miles per gallon}$.

   • Option B: Passes through (10, 300).
     Slope $m = \frac{\text{Distance}}{\text{Gas}} = \frac{300}{10} = 30 \, \text{miles per gallon}$.

   • Option C: Passes through approximately (1, 300).
     Slope $m = \frac{\text{Distance}}{\text{Gas}} = \frac{300}{1} = 300 \, \text{miles per gallon}$.

   • Option D: Data missing; cannot analyze.

Key Observations:

• The relationship between distance ($D$) and gas ($G$) is realistic if the slope is constant and reasonable (e.g., around 10–30 miles per gallon for typical vehicles).
• Option B seems realistic, with a slope of $30$ miles per gallon, which is typical for an efficient vehicle.

Conclusion:

The graph in Option B best represents the relationship between distance ($D$) and gas used ($G$), as the slope indicates an efficient but realistic fuel consumption rate.

Would you like to go over how to calculate slopes or interpret linear graphs in greater detail?
Here are 5 related questions you might explore:

1. How do you derive the equation of a line from two points?
2. How does the slope of a line relate to real-world rates like speed or efficiency?
3. What are some other examples of linear relationships in everyday life?
4. How can you identify proportional relationships from a graph?
5. How does changing the slope affect the appearance of a graph?

Tip: When analyzing graphs, always confirm key points like the origin and labeled values to ensure proper interpretation!