To determine the y-intercept in this situation, we need to analyze the linear relationship between the miles traveled (x) and the total fee (y).
From the data provided, we can see that the total fee increases as the number of miles increases. The cab fare is likely made up of a base fee (the y-intercept) and a cost per mile.
Let's look at the points to find the slope and the y-intercept:
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Calculate the slope (cost per mile):
- Use two points: (2, 17.00) and (5, 21.50)
- The slope (m) is calculated as: \[ m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{21.50 - 17.00}{5 - 2} = \frac{4.50}{3} = 1.50 \] So, the cost per mile is $1.50.
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Now, to find the y-intercept (the base fee), we can use one of the points and the slope. Let's use the point (2, 17.00): \[ y = mx + b \quad \text{(where b is the y-intercept)} \] Plugging in the values: \[ 17.00 = 1.50(2) + b \] \[ 17.00 = 3.00 + b \] \[ b = 17.00 - 3.00 = 14.00 \]
This means that when x (miles traveled) is 0, the total fee (y) will be $14.00, which represents the base fare for hailing the cab.
Thus, the correct interpretation of the y-intercept in this situation is:
When the cab travels 0 miles, the total fee will be $14.00.