The graph shows the relationship between the distance traveled (in miles) and the gas used (in gallons) by a car. To determine what the "rate of change" represents in this situation, let’s analyze the graph:

1. Rate of Change: It is the slope of the line, which is calculated as the change in the y-values (distance in miles) divided by the change in the x-values (gas used in gallons).

   Using two points from the graph:

   • Point 1: (0, 0)
   • Point 2: (4, 100)

   $\text{Rate of change} = \frac{\text{Change in y (distance)}}{\text{Change in x (gas used)}} = \frac{100 - 0}{4 - 0} = 25 \text{ miles per gallon.}$

2. Interpretation: The rate of change represents the car's miles per gallon (mpg), which is the fuel efficiency of the car.

Final Answer:

The rate of change represents miles per gallon, which describes how far the car can travel using one gallon of gas.

Would you like more details or explanations about how this is calculated?

Here are 5 related questions you might explore:

1. How do you calculate the slope of a line from any two points?
2. What does a steeper slope in such a graph represent?
3. How is the concept of rate of change applied in other real-life scenarios?
4. What would happen if the graph wasn’t linear—how would the interpretation of rate of change change?
5. Can you use this graph to estimate how much gas is required for a specific distance?

Tip: The slope (rate of change) is crucial in understanding relationships in linear graphs; always identify two clear points for accurate calculations!