Final answer:
By calculating the slope of the line using the given points and finding the y-intercept, we can determine the equation that represents the cost in relation to the miles. However, the calculated equation does not match the answer choices provided, indicating there might be a mistake in the question or options.
Step-by-step explanation:
To find the linear equation that represents the given situation, we need to understand the relationship between the cost (y) and the miles (x). The data provided are the pairs (5, 8.50), (8, 15.25), (12, 22.00), and (20, 31.00). To determine which equation is the correct representation, we can calculate the slope of the line by finding the change in y over the change in x (rise over run).
For instance, if we use the points (5, 8.50) and (8, 15.25), the slope (m) can be calculated as:
m = (15.25 - 8.50) / (8 - 5) = 6.75 / 3 = 2.25
Now, we need to find the y-intercept (b). We can do this by substituting the values of one of the points into the equation y = mx + b, for x and y.
Using (5, 8.50) and m = 2.25:
8.50 = 2.25 * 5 + b
b = 8.50 - (2.25 * 5)
b = 8.50 - 11.25 = -2.75
Therefore, the linear equation is y = 2.25x - 2.75, which is not one of the options given, so it seems there is a mistake in the question or the answer choices. To provide an accurate solution to the student, we would need to revisit the data or the answer options provided.