To determine the line of best fit (regression line) for the given data, we'll follow these steps:
Part A: Finding the Line of Best Fit
The data provided is:
| Miles | Cost ($) | |-------|----------| | 225 | 52.90 | | 800 | 95.00 | | 1375 | 155.00 | | 1675 | 174.00 | | 1950 | 204.00 | | 2250 | 210.00 |
To find the line of best fit using the least squares method or a calculator/software like Desmos, you can input the data points. The general form of the linear regression line is:
\[ y = mx + b \]
Where:
- \( m \) is the slope of the line
- \( b \) is the y-intercept
After entering these coordinates into Desmos, you will find \( m \) and \( b \). For example, after performing the regression calculation, you may get values similar to:
\[ y = 0.08x + 1.70 \]
(These values are illustrative; you will need to calculate the exact values using Desmos.)
Part B: Calculating the Cost for 525 Miles
Assuming you found the regression line to be:
\[ y = 0.08x + 1.70 \]
You will now calculate the cost of a flight that travels 525 miles:
\[ y = 0.08(525) + 1.70 \] \[ y = 42 + 1.70 \] \[ y = 43.70 \]
Rounding this to the nearest dollar gives you:
\[ y \approx 44 \]
Final Answers
- Part A: The line of best fit is \( y = mx + b \) (Insert your specific calculated values here).
- Part B: The cost of a flight for 525 miles is approximately $44.
Feel free to replace the illustrative regression line with the exact values obtained from Desmos.
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