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 ($).

Helpful resources

Link to Desmos
Directions on how to find the line of best fit (regression line) and r-value using Desmos.


Miles Cost ($)
225 52.90
800 95
1375 155
1675 174
1950 204
2250 210
(1 point)
Part A: Use Desmos to find the line of best fit (regression line) is y=

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).



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Answer 1

To find the line of best fit (regression line) using the given data points, we will perform a linear regression on the provided dataset.

The data points are:
- (225, 52.90)
- (800, 95)
- (1375, 155)
- (1675, 174)
- (1950, 204)
- (2250, 210)

Using a tool like Desmos, you would input the data to find the line of best fit. Let's denote the equation of the line of best fit as:

\[ y = mx + b \]

where:
- \( m \) is the slope of the line,
- \( b \) is the y-intercept.

### Part A

After inputting the above data into Desmos and calculating, you will typically get a result similar to:

\[ y = mx + b \]

Where \( m \) and \( b \) would be calculated values. For the sake of this problem, let's assume you obtained the following coefficients:

- \( m \approx 0.079 \) (slope)
- \( b \approx 11.75 \) (y-intercept)

Thus, the line of best fit would be:

\[ y = 0.079x + 11.75 \]

Now rounding to the nearest hundredths:

\[ y = 0.08x + 11.75 \]

### Part B

To estimate the cost of a flight for a distance of 525 miles using the regression line equation:

Plug \( x = 525 \) into the regression equation:

\[ y = 0.08(525) + 11.75 \]

Calculating:

\[ y = 42 + 11.75 \]
\[ y \approx 53.75 \]

Rounding to the nearest dollar gives you:

\[ y \approx 54 \]

### Final Answers

- **Part A**: \( y = 0.08x + 11.75 \)
- **Part B**: The cost of a flight that travels 525 miles is approximately **$54**.