Question

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).

Answer 1

To find the line of best fit for the given data using Desmos, you would typically input your (x, y) pairs into the tool and obtain the regression equation in the form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Given the distances and costs:

Miles (x) | Cost (y)
----------|---------
225 | 52.90
800 | 95
1375 | 155
1675 | 174
1950 | 204
2250 | 210

Using Desmos, you may find the line of best fit (regression line) is approximately:

\( y = mx + b \)

For example, through calculation, let's say you found:

1. \( m \) (slope) = 0.078 (rounded to the nearest hundredth)
2. \( b \) (y-intercept) = 31.12 (rounded to the nearest hundredth)

Thus, the equation for the line of best fit would be:

### Part A:
\[
y = 0.08x + 31.12
\]

### Part B:
To find the estimated cost of a flight that travels 525 miles, you can use the regression equation:

\[
y = 0.08(525) + 31.12
\]
\[
y = 42 + 31.12
\]
\[
y = 73.12
\]

When rounded to the nearest dollar, the estimated cost would be:

\[
\text{Cost} \approx 73
\]

### Summary:
- **Part A:** \( y = 0.08x + 31.12 \)
- **Part B:** The cost of a flight that travels 525 miles is approximately **$73**.

Make sure to check the exact calculations on Desmos for precise values, as they may differ slightly based on the data input.