Question

2. The cost of a flight is related to the distance traveled. Thus, the farther you fly, the more you pay for the flight. Use the data to answer the questions, keep in mind that x
is the distance in miles and y
is the cost in dollars ($).

Miles Cost ($)
225 52.90
800 95
1375 155
1675 174
1950 204
2250 210
Part A: Use Desmos to find the line of best fit (regression line) is y= FILL IN
x +
. Round your answer to the nearest hundredths.
Part B: Using the equation you found above (rounded regression line), the cost of a flight that travels 525 miles is $
(Round to the nearest dollar).

Answer 1

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.