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.
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