Question

1. the table below shows the altitude of a plane once it begins its descent to a runway. a) write an equation to model the data using linear regression. b) find the height of the plane after 8 minutes. c) how long will it take the plane to land? about minutes

Explanation:

Step1: Recall linear regression equation form

The general form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. We can use two - point form to find the slope. Let $(x_1,y_1)=(0,28500)$ and $(x_2,y_2)=(1,26378)$. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{26378 - 28500}{1-0}=- 2122$. When $x = 0$, $y=b = 28500$. So the equation is $y=-2122x + 28500$.

Step2: Find height at 8 minutes

Substitute $x = 8$ into the equation $y=-2122x + 28500$. Then $y=-2122\times8+28500=-16976 + 28500=11524$ feet.

Step3: Find time to land

The plane lands when $y = 0$. Set $y = 0$ in the equation $0=-2122x+28500$. Solve for $x$: $2122x=28500$, so $x=\frac{28500}{2122}\approx13.43$ minutes.

Answer:

a) $y=-2122x + 28500$
b) 11524 feet
c) 13.43