Final answer:
The best two points to represent the relationship between distance and cost are those which show a consistent linear relationship, identified by calculating the slope, or rate of change, between the two variables. This allows for a simple yet accurate representation of the cost per mile.
Step-by-step explanation:
When selecting two points to best represent the relationship between the number of miles and the cost of a trip on a graph, it is important to look for points that suggest a linear relationship. In your case, we are looking at pairs of points such as (10,5) and (250,120), or (40,10) and (250,145), among others. A linear relationship can be depicted by a straight line when graphed, and it indicates a constant rate of change between the two variables.
To determine which two points are best, we calculate the rate of change or slope. The slope represents the cost per mile and is calculated by dividing the change in cost by the change in distance. For example, with the points (10,5) and (250,120), the slope would be (120-5) / (250-10), which is 115/240. This provides us with a rate of cost per mile. We assume that the relationship between distance and cost is linear because that allows us to predict costs for different distances using a simple multiplication.
It's important to choose points that show a consistent slope (or rate), which implies a linear relationship between distance and cost. The points should not have outliers or drastic changes that do not fit the overall pattern of the data. By doing so, the graph will better represent the actual relationship between mileage and trip cost.