To solve this, we need to analyze the relationship between the cost (C) and the distance flown (D) based on the given graphs and determine which graph correctly represents the equation for this relationship.

Step-by-step Approach:

The general form of a linear equation is: $C = mD + b$ Where:

• $C$ is the cost.
• $D$ is the distance.
• $m$ is the slope (rate of change of cost per unit of distance).
• $b$ is the y-intercept (cost when the distance is 0).

In each graph:

• The line starts at the origin (0, 0), meaning that $b = 0$, since the cost is $0 when no distance is flown.

The only thing we need to focus on is the slope of each line, which will determine how the cost increases as the distance increases.

Let's calculate the slopes for the given options:

1. Option A:

   • Coordinates: (0, 0) and (150, 28.5)
   • Slope: $m = \frac{28.5 - 0}{150 - 0} = \frac{28.5}{150} = 0.19$

2. Option B:

   • Coordinates: (0, 0) and (75, 57)
   • Slope: $m = \frac{57 - 0}{75 - 0} = \frac{57}{75} = 0.76$

3. Option C:

   • Coordinates: (0, 0) and (100, 38)
   • Slope: $m = \frac{38 - 0}{100 - 0} = \frac{38}{100} = 0.38$

Conclusion:

• Each option represents a different rate of increase in cost as the distance increases.
• Based on the options, the graph with the correct slope should reflect the intended cost per mile.

Would you like a further breakdown of how to analyze this or confirm your selected choice?

Here are 5 related questions:

1. How can you derive a linear equation from any two points on a graph?
2. What does the slope represent in the context of cost and distance?
3. How would the graph look if there was an initial fixed cost, regardless of distance?
4. How does changing the slope affect the steepness of the line on the graph?
5. Why does the line start at the origin in this context?

Tip: Always check the units on the axes when interpreting graphs for clarity!